I. Petras
This paper deals with fractional-order controllers. We outline mathematical description of fractional controllers and methods of their synthesis and application. Synthesis method is a modified root locus method for fractional-order systems and fractional-order controllers. In the next section we describe how to apply the fractional controller on control systems.
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Novel closed-loop controllers for fractional linear quadratic tracking systems
本文提出了一种新颖的闭环控制器方法，用于解决分数线性二次跟踪系统的最优控制问题，并通过示例验证了其有效性。
This paper deals with the fractional-order controllers and their possible hardware realization based on PIC microprocessor and numerical algorithm coded in PIC Basic. The mathematical description of the digital fractional -order controllers and approximation in the discrete domain are presented. An example of realization of the particular case of digital fractional-order PID controller is shown and described.
We have witnessed the emergence of several controller parameterizations and the corresponding synthesis methods, including Youla, system level, input-output, and many other new proposals. Meanwhile, under the same synthesis method, there are multiple realizations to adopt. Different synthesis methods/realizations target different plants/scenarios. Except for some case-by-case studies, we don't currently have a unified framework to understand their relationships. To address the issue, we show that existing controller synthesis methods and realization proposals are all special cases of a simple …
This paper is concerned with model reference adaptive controller design for a class of nonlinear fractional order systems. Recent works on this topic rarely include direct methods and they are mostly based on indirect methods where the frequency distributed model is used to prove the stability of the closed loop system. Since the chain rule cannot be applied in fractional derivations, in order to prove the lyapunov stability here fractional inequalities are used. Finally, by means of a numerical example, the controller performance is demonstrated.
This paper deals with designing a robust fixed-order dynamic output feedback controller for uncertain fractional order linear time invariant (FO-LTI) systems by means of linear matrix inequalities (LMIs). Our purpose is to design a low order controller that stabilizes the fractional-order linear system in the presence of model uncertainties. No limitative constraint on the state space matrices of the uncertain system is assumed in the design procedure. Furthermore, adopting the most complete model of linear controller, with direct feedthrough parameter, does not disturb the LMI-based approach …
In this paper we will present a mathematical description and analysis of a fractional-order regulated system in the state space and the state-space controller design based on placing the closed-loop poles on the complex plane. Presented are the results of simulations and stability investigation of this system.
The objective of this paper is to solve the controller synthesis problem for bisimulation equivalence in a wide variety of scenarios including discrete-event systems, nonlinear control systems, behavioral systems, hybrid systems and many others. This will be accomplished by showing that the arguments underlying proofs of existence and methods for the construction of controllers are extraneous to the particular class of systems being considered and thus can be presented in greater generality.
This paper presents necessary and sufficient conditions for deriving a strictly proper dynamic controller which satisfies the negative imaginary output feedback control problem. Our synthesis method divides the output feedback control problem into a state feedback problem and a dual output injection problem. Thus, a controller is formed using the solutions to a pair of dual algebraic Riccati equations. Finally, an illustrative example is offered to show how this method may be applied.
A novel conformal mapping based Fractional Order (FO) methodology is developed in this paper for tuning existing classical (Integer Order) Proportional Integral Derivative (PID) controllers especially for sluggish and oscillatory second order systems. The conventional pole placement tuning via Linear Quadratic Regulator (LQR) method is extended for open loop oscillatory systems as well. The locations of the open loop zeros of a fractional order PID (FOPID or PIλDμ) controller have been approximated in this paper vis-à-vis a LQR tuned conventional integer order PID controller, to achieve equiva…
We have witnessed the emergence of several controller parameterizations and the corresponding synthesis methods, including Youla, system level, input-output, and many other new proposals. Meanwhile, under the same synthesis method, there are multiple realizations to adopt. Different synthesis methods/realizations target different plants/scenarios. Also, various robust results are proposed to deal with different perturbed system structures. Except for some case-by-case studies, we don't currently have a unified framework to understand their relationships. To address the issue, we show that exis…
This paper proposes the application of fractional-order PID (FOPID) controller for output voltage control of boost converters. For this purpose, parameters of the FOPID controller are calculated such that the Integral Absolute Error (IAE) of the variations of the output voltage is minimized. Since the search space is very large in dealing with such an optimization problem, the Artificial Bee Colony (ABC) algorithm is used for optimal tuning the parameters of the FOPID controller. Simulations, which are performed by using the complete non-minimum phase model of the boost converter, confirm the …
This paper presents a new data-driven controller synthesis based on the Koopman operator and the extended $\mathcal{H}_2$ norm characterization of discrete-time linear systems. We model dynamical systems as polytope sets which are derived from multiple data-driven linear models obtained by the finite approximation of the Koopman operator and then used to design robust feedback controllers combined with the $\mathcal{H}_2$ norm characterization. The use of the $\mathcal{H}_2$ norm characterization is aimed to deal with the model uncertainty that arises due to the nature of the data-driven setti…
Designing System Level Synthesis Controllers for Nonlinear Systems with Stability Guarantees
针对全驱动非线性系统，本文用多项式逼近动力学并结合神经网络优化 SLS 控制器，在无需 Lyapunov 函数的情况下保证稳定性，并给出稳定域与控制成本界，实验性能优于反馈线性化。
Robust Controller Synthesis under Markovian Mode Switching with Periodic LTV Dynamics
本文研究周期时变 Markov 跳变线性系统的鲁棒控制，提出基于 LMI 的综合框架，通过放宽 Lyapunov 下降条件实现二次代价最小化与吸引域最大化，并经仿真验证其稳定性和容错控制适用性。
We consider optimal distributed controller synthesis for an interconnected system subject to communication constraints, in linear quadratic settings. Motivated by the problem of finite heavy duty vehicle platooning, we study systems composed of interconnected subsystems over a chain graph. By decomposing the system into orthogonal modes, the cost function can be separated into individual components. Thereby, derivation of the optimal controllers in state-space follows immediately. The optimal controllers are evaluated under the practical setting of heavy duty vehicle platooning with communicat…
The continuous and discrete time Linear Quadratic Regulator (LQR) theory has been used in this paper for the design of optimal analog and discrete PID controllers respectively. The PID controller gains are formulated as the optimal state-feedback gains, corresponding to the standard quadratic cost function involving the state variables and the controller effort. A real coded Genetic Algorithm (GA) has been used next to optimally find out the weighting matrices, associated with the respective optimal state-feedback regulator design while minimizing another time domain integral performance index…
This paper presents a fractional-order framework for control of blood pressure. A new perspective is explored to control the blood pressure in lieu of the conventional control framework. A multi-variable scenario is adopted to control two outputs: Mean Arterial Blood Pressure (MABP) and Cardiac Output (CO) simultaneously.
Output-Feedback Controller Synthesis for Dissipativity and $H_2$ Performance of Autoregressive Systems from Noisy Input-Output Data
本文提出一种基于数据的输出反馈控制器综合方法，用于离散时间线性时不变系统，旨在实现给定二次供应率的耗散性或指定H₂性能水平。
Convex Constrained Controller Synthesis for Evolution Equations
本文提出一个针对受约束线性系统（含偏微分和积分方程）的凸控制器综合框架，采用无限维希尔伯特空间和输出反馈SLS，实现先优化后离散化，并在线性玻尔兹曼方程上验证了其有效性。
Relaxed conditions are given for stability of a feedback system consisting of an exponentially stable multi-input multi-output nonlinear plant and an integral controller. Roughly speaking, it is shown that if the composition of the plant equilibrium input-output map and the integral feedback gain is infinitesimally contracting, then the closed-loop system is exponentially stable if the integral gain is sufficiently low. The main result is illustrated with an application arising in frequency control of AC power systems. We demonstrate how the contraction condition can be checked computationally…
A structure exploiting SDP solver for robust controller synthesis
本文提出在结构利用的KYP-SDP求解器中引入Lyapunov矩阵半定约束，以解决现有专用求解器无法支持鲁棒控制器综合的问题。
This paper considers the robustness analysis and distributed $\mathcal{H}_{\infty}$ (H-infinity) controller synthesis for a platoon of connected vehicles with undirected topologies. We first formulate a unified model to describe the collective behavior of homogeneous platoons with external disturbances using graph theory. By exploiting the spectral decomposition of a symmetric matrix, the collective dynamics of a platoon is equivalently decomposed into a set of subsystems sharing the same size with one single vehicle. Then, we provide an explicit scaling trend of robustness measure $γ$-gain, a…
We demonstrate the use of a new, control-oriented notion of finite state approximation for a particular class of hybrid systems. Specifically, we consider the problem of designing a stabilizing binary output feedback switching controller for a pair of unstable homogeneous second order systems. The constructive approach presented in this note, in addition to yielding an explicit construction of a deterministic finite state approximate model of the hybrid plant, allows us to efficiently establish a useable upper bound on the quality of approximation, and leads to a discrete optimization problem …
Robust controller synthesis attracts reviving research interest, driven by the rise of learning-based systems where uncertainty and perturbation are ubiquitous. Facing an uncertain situation, a robustly stabilizing controller should maintain stability while operating under a perturbed system deviating from its nominal specification. There have been numerous results for robust controller synthesis in multiple forms and with various goals, including mu-synthesis, robust primal-dual Youla, robust input-output, and robust system level parameterizations. However, their connections with one another …
This paper is concerned with a linear fractional representation approach to the synthesis of linear coherent quantum controllers for a given linear quantum plant. The plant and controller represent open quantum harmonic oscillators and are modelled by linear quantum stochastic differential equations. The feedback interconnections between the plant and the controller are assumed to be established through quantum bosonic fields. In this framework, conditions for the stabilization of a given linear quantum plant via linear coherent quantum feedback are addressed using a stable factorization appro…
Whale Optimization Algorithms based fractional order fuzzy PID controller for Depth of Anesthesia
针对麻醉深度控制中的非线性与患者生理参数不确定性，提出用WOA优化参数的FOFPID与FOPID，并基于8例患者的药效动力学和药代动力学模型验证FOFPID性能更优。
Synthesizing controllers for large, complex, and distributed systems is a challenging task. Numerous proposed methods exist in the literature, but it is difficult for practitioners to apply them -- most proposed synthesis methods lack ready-to-use software implementations, and existing proprietary components are too rigid to extend to general systems. To address this gap, we develop SLSpy, a framework for controller synthesis, comparison, and testing. SLSpy implements a highly extensible software framework which provides two essential workflows: synthesis and simulation. The workflows are buil…
Performance Comparison of Optimal Fractional Order Hybrid Fuzzy PID Controllers for Handling Oscillatory Fractional Order Processes with Dead Time
本文研究了基于模糊逻辑的PID控制器，通过不同形式的模糊推理组合设计了分数阶混合模糊PID控制器，用于处理具有死区的分数阶过程，比较了不同控制器结构的性能。
Optimum Weight Selection Based LQR Formulation for the Design of Fractional Order PIλDμ Controllers to Handle a Class of Fractional Order Systems
本文提出基于LQR技术的分数阶PID或PIλDμ控制器时间域最优整定方法，用于处理具有单非整数阶元件的分数阶系统，通过优化权值矩阵提升系统响应性能。
This paper investigates the robust stabilisation of a class of fractional-order non-linear systems via fixed-order dynamic output feedback controller in terms of linear matrix inequalities (LMIs). The systematic stabilisation algorithm design for low-order controller based on direct Lyapunov approach is proposed. In the presented algorithm the conditions containing the bilinear variables are decoupled into separate conditions without imposing equality constraints or considering an iterative search of the controller parameters. There is no any limiting constraint on the state space matrices and…
Generalised Regret Optimal Controller Synthesis for Constrained Systems
本文提出约束系统的广义后悔最优控制器综合方法，涵盖动态后悔与竞争比框架，支持扰动逐点有界及状态输入约束，数值验证其性能优于经典$\u210b_2$、$\u210b_\infty$控制器。
Controller Synthesis for Safety and Reachability via Approximate Bisimulation
本文利用近似双模拟抽象方法，针对安全性和可达性规范设计控制器，通过抽象控制器综合与具体化过程保证正确性，并给出与最优控制器的距离估计。
Discrete-Time Fractional-Order PID Controller: Definition, Tuning, Digital Realization and Experimental Results
本文提出离散时间分数阶PID控制器，讨论其特性与应用，开发两种调参方法，展示其在复杂控制问题中的高性能表现。
We consider the problem of how to deploy a controller to a (networked) cyber-physical system (CPS). Controlling a CPS is an involved task, and synthesizing a controller to respect sensing, actuation, and communication constraints is only part of the challenge. In addition to controller synthesis, one should also consider how the controller will be incorporated within the CPS. Put another way, the cyber layer and its interaction with the physical layer need to be taken into account. In this work, we aim to bridge the gap between theoretical controller synthesis and practical CPS deployment. We …
On moment relaxations for linear state feedback controller synthesis with non-convex quadratic costs and constraints
本文提出一种基于状态和输入矩矩阵的线性状态反馈控制器设计方法，通过将非凸约束松弛为期望约束来处理非凸代价与约束，并揭示了凸化变量与矩矩阵块的对应关系。
Controller Synthesis for Robust Invariance of Polynomial Dynamical Systems using Linear Programming
针对有界扰动和输入约束的多项式动力系统，提出一种通过线性规划迭代求解控制器与多面体不变集的综合方法。
Dynamic Output-Feedback Controller Synthesis for Dissipativity and $H_2$ Performance from Noisy Input-State Data
本文针对噪声输入-状态数据，提出动态输出反馈控制器综合方法，实现系统 dissipativity 和 $H_2$ 性能，通过线性矩阵不等式参数化标量变量，非保守地完成控制器设计。
This manuscript discusses a scalable controller synthesis method for networked systems with a large number of identical subsystems based on the H-infinity control framework. The dynamics of the individual subsystems are described by identical linear time-invariant delay differential equations and the effect of transport and communication delay is explicitly taken into account. The presented method is based on the result that, under a particular assumption on the graph describing the interconnections between the subsystems, the H-infinity norm of the overall system is upper bounded by the robus…
In this paper, a fractional Lotka-Volterra mathematical model for a bioreactor is proposed and used to fit the data provided by a bioprocess known as continuous fermentation of Zymomonas mobilis. The model contemplates a time-delay $τ$ due to the dead-time in obtaining the measurement of biomass $x(t)$. A Hopf bifurcation analysis is performed to characterize the inherent self oscillatory experimental bioprocess response. As consequence, stability conditions for the equilibrium point together with conditions for limit cycles using the delay $τ$ as bifurcation parameter are obtained. Under the …
Permissive Controller Synthesis for Probabilistic Systems
本文提出了一种新的控制器合成方法，用于概率系统模型中的随机双人游戏，旨在生成鲁棒且灵活的控制器，通过多策略减少惩罚并确保系统属性满足。
This paper addresses the consensus of a class of uncertain nonlinear fractional-order multi-agent systems (FOMAS). First a fractional non-fragile dynamic output feedback controller is put forward via the output measurements of neighboring agents, then appropriate state transformation reduced the consensus problem to a stability one. A sufficient condition based on direct Lyapunov approach, for the robust asymptotic stability of the transformed system and subsequently for the consensus of the main system is presented. Additionally, utilizing S-procedure and Schur complement, the systematic stab…
Frequency Domain Design of Fractional Order PID Controller for AVR System Using Chaotic Multi-objective Optimization
本文提出一种基于混沌多目标优化的分数阶PID控制器设计方法，用于AVR系统，通过改进的NSGA-II算法优化控制器参数，保证系统稳定性和鲁棒性。
A class of non-linear fractional-order system stabilisation via fixed-order dynamic output feedback controller
本文研究了一类非线性分数阶系统的鲁棒稳定化问题，采用线性矩阵不等式（LMIs）方法设计了基于直接Lyapunov方法的低阶控制器系统稳定化算法。该算法将包含双线性变量的条件分解为独立条件，无需施加等式约束或考虑控制器参数的迭代搜索。没有对状态空间矩阵施加任何限制，并假设了最完整的输出反馈控制器。仿真结果证明了所提设计的有效性和简便性。
We propose a framework for synthesizing a feedback control policy that maximizes the region of attraction (ROA) of a closed-loop nonlinear dynamical system. Our synthesis technique relies on stochastic optimization, which involves computation of an objective function capturing the ROA for a feedback control law. We employ a machine learning technique based on deep neural network to estimate the ROA for a given feedback controller. Overall, our technique is capable of synthesizing a controller co-optimizing traditional control objectives like LQR cost together with ROA. We demonstrate the effic…
Biological and advanced cyberphysical control systems often have limited, sparse, uncertain, and distributed communication and computing in addition to sensing and actuation. Fortunately, the corresponding plants and performance requirements are also sparse and structured, and this must be exploited to make constrained controller design feasible and tractable. We introduce a new "system level" (SL) approach involving three complementary SL elements. System Level Parameterizations (SLPs) generalize state space and Youla parameterizations of all stabilizing controllers and the responses they ach…
Control of systems with operating condition-dependent dynamics, including control moment gyroscopes, often requires operating condition-dependent controllers to achieve high control performance. The aim of this paper is to develop a frequency response data-driven linear parameter-varying control design approach for single-input single-output systems, which allows improved performance for a control moment gyroscope. A stability theory using closed-loop frequency response function data is developed, which is subsequently used in a synthesis procedure that guarantees local stability and performan…
Multi-objective robust controller synthesis with integral quadratic constraints in discrete-time
本文提出一种离散时间下基于动态积分二次约束的多目标鲁棒控制器综合框架，通过最小化多种性能指标（如H∞范数、能量到峰值增益等）来约束输出峰值，数值示例验证了其有效性。
Synthesis for Constrained Nonlinear Systems using Hybridization and Robust Controllers on Simplices
提出一种基于混合化（非线性动力学的混合抽象）的方法，通过在状态空间三角剖分的每个单纯形上设计并协调局部鲁棒仿射控制器，实现对约束非线性系统的控制器综合。
Controller synthesis for input-state data with measurement errors
该研究面向仅含测量误差的输入-状态数据，提出基于线性矩阵不等式的线性系统状态反馈控制器设计方法，并建立能量界情形与公共 Lyapunov 函数鲁棒镇定的等价关系。
Control Strategy for Anaesthetic Drug Dosage with Interaction Among Human Physiological Organs Using Optimal Fractional Order PID Controller
本文提出利用最优分数阶PID控制器优化麻醉药物输注模型，通过粒子群优化算法确定控制器参数，实现更高效的药物输注控制，减少药物用量并提高系统鲁棒性。
Synthesis of anisotropic suboptimal controllers by convex optimization
针对具有不精确已知概率分布的随机扰动的线性离散时不变系统，提出基于各向异性范数的次优控制器设计方法，通过凸优化求解固定阶动态输出反馈补偿器。
This paper considers the synthesis of optimal safe controllers based on density functions. We present an algorithm for robust constrained optimal control synthesis using the duality relationship between the density function and the value function. The density function follows the Liouville equation and is the dual of the value function, which satisfies Bellman's optimality principle. Thanks to density functions, constraints over the distribution of states, such as safety constraints, can be posed straightforwardly in an optimal control problem. The constrained optimal control problem is then s…
In this paper we consider the safety verification and safe controller synthesis problems for nonlinear control systems. The Control Barrier Certificates (CBC) approach is proposed as an extension to the Barrier certificates approach. Our approach can be used to characterize the control invariance of a given set in terms of safety of a general nonlinear control system subject to input constraints. From the point of view of controller design, the proposed method provides an approach to synthesize a safe control law that guarantees that the trajectories of the system starting from a given initial…
Dynamic Output-Feedback Controller Synthesis for Dissipativity and $H_2$ Performance from Noisy Input-Output Data
针对离散时间线性时不变系统，提出利用含噪输入输出数据直接综合动态输出反馈控制器的方法，以实现给定二次供给率下的耗散性或$H_2$性能，方法基于线性矩阵不等式且无保守性。
We present a new method for the automated synthesis of digital controllers with formal safety guarantees for systems with nonlinear dynamics, noisy output measurements, and stochastic disturbances. Our method derives digital controllers such that the corresponding closed-loop system, modeled as a sampled-data stochastic control system, satisfies a safety specification with probability above a given threshold. The proposed synthesis method alternates between two steps: generation of a candidate controller pc, and verification of the candidate. pc is found by maximizing a Monte Carlo estimate of…
Feedback Refinement Relations for the Synthesis of Symbolic Controllers
本文提出了一种抽象和细化方法，用于自动控制器合成以满足通用预定义规范。控制器仅需量化状态信息，通过静态量化器与系统接口，并通过反馈细化关系确保鲁棒性和可证明性。
System Level Synthesis (SLS) parametrization facilitates controller synthesis for large, complex, and distributed systems by incorporating system level constraints (SLCs) into a convex SLS problem and mapping its solution to stable controller design. Solving the SLS problem at scale efficiently is challenging, and current attempts take advantage of special system or controller structures to speed up the computation in parallel. However, those methods do not generalize as they rely on the specific system/controller properties. We argue that it is possible to solve general SLS problems more effi…
Although variable-speed three-blade wind turbines are nowadays quite popular, their control remains a challenging task. We propose a new easily implementable model-free control approach with the corresponding intelligent controllers. Several convincing computer simulations, including some fault accommodations, shows that model-free controllers are more efficient and robust than classic proportional-integral controllers.
Automatic Synthesis of Switching Controllers for Linear Hybrid Automata
针对线性混合自动机，提出基于多面体抽象状态空间的符号不动点程序，自动生成满足安全目标的切换控制器，并证明每次迭代的终止性。
Controller Synthesis for Discrete-Time Polynomial Systems via Occupation Measures
本文通过占用测度方法为离散时间多项式动力系统设计非线性状态反馈控制器，将控制器合成问题转化为无限维线性规划问题，并通过松弛为有限维半正定规划问题，从而提取非线性控制器，该方法具有计算复杂度低且可扩展性强的优势。
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