For a partially unknown linear systems, we present a systematic control design approach based on generated data from measurements of closed-loop experiments with suitable test controllers. These experiments are used to improve the achieved performance and to reduce the uncertainty about the unknown parts of the system. This is achieved through a parametrization of auspicious controllers with convex relaxation techniques from robust control, which guarantees that their implementation on the unknown plant is safe. This approach permits to systematically incorporate available prior knowledge about the system by employing the framework of linear fractional representations.
This paper presents a novel adaptive control methodology for uncertain systems with time-varying unknown parameters and time-varying bounded disturbance. The adaptive controller ensures uniformly bounded transient and asymptotic tracking for system's both signals, input and output, simultaneously. The performance bounds can be systematically improved by increasing the adaptation gain. Simulations of a robotic arm with time-varying friction verify the theoretical findings.
We consider the decentralized control of a discrete-time time-varying linear system subject to additive disturbances and polyhedral constraints on the state and input trajectories. The underlying system is composed of a finite collection of dynamically coupled subsystems, where each subsystem is assumed to have a dedicated local controller. The decentralization of information is expressed according to sparsity constraints on the state measurements that each local controller has access to. We investigate the design of decentralized controllers that are affinely parameterized in their measuremen…
In this paper we propose a constrained guaranteed cost robust model predictive controller (GCMPC) for uncertain discrete time systems. This controller was developed based on a quadratic cost functional and guarantee robustness with respect to quadratically bound uncertainties. Such a class of problems is currently intractable by Min-Max Robust Model Predictive Controllers without polytopic approximations of the uncertainties. The proposed technique is computationally more efficient then an enumeration-based approach and requires only a Quadratically Constrained Quadratic Problem (QCQP) optimiz…
This thesis presents fuzzy-L1 adaptive controller and Model Reference Adaptive Control (MRAC) with Prescribed Performance Function (PPF) as two adaptive approaches for high nonlinear systems as two original contribution to the literature. L1 adaptive controller has a structure that allows decoupling between robustness and adaption owing to the use of a low pass filter with adjustable gain in the feedback loop. A practical new fuzzy based approach for the tuning of the feedback filter of L1 adaptive controller is proposed. The fuzzy controller is optimally tuned using Particle Swarm Optimizatio…
Adaptive cooperative tracking control with prescribed performance function (PPF) is proposed for high-order nonlinear multi-agent systems. The tracking error originally within a known large set is confined to a smaller predefined set using this approach. Using output error transformation, the constrained system is relaxed and mapped to an unconstrained one. The controller is conceived under the assumption that the agents' nonlinear dynamics are unknown and the perceived network is structured and strongly connected. Under the proposed controller, all agents track the trajectory of the leader no…
In this paper, we propose state- and static output-feedback generalized guaranteed cost control (GCC) approaches for discrete-time linear systems subject to norm-bounded structured parametric uncertainties. This method enables the convex synthesis for a more general class of systems, where uncertainties are uncorrelated block diagonal, and no feed-through uncertainty is multiplicative with control input ones. It also provides necessary and sufficient conditions for state-feedback and sufficient conditions for static output-feedback. We also present a comparative study among the proposed contro…
Networked Control Systems (NCSs) often suffer from random packet dropouts which deteriorate overall system's stability and performance. To handle the ill effects of random packet losses in feedback control systems, closed over communication network, a state feedback controller with predictive gains has been designed. To achieve improved performance, an optimization based controller design framework has been proposed in this paper with Linear Matrix Inequality (LMI) constraints, to ensure guaranteed stability. Different conflicting objective functions have been optimized with Non-dominated Sort…
We propose and analyze a real-time model predictive control (MPC) scheme that utilizes stored data to improve its performance by learning the value function online with stability guarantees. For linear and nonlinear systems, a learning method is presented that makes use of basic analytic properties of the cost function and is proven to learn the MPC control law and the value function on the limit set of the closed-loop state trajectory. The main idea is to generate a smart warm start based on historical data that improves future data points and thus future warm starts. We show that these warm …
In this paper we investigate feedback control techniques for the COVID-19 pandemic which are able to guarantee that the capacity of available intensive care unit beds is not exceeded. The control signal models the social distancing policies enacted by the local government. We propose a control design based on the bang-bang funnel controller which is robust with respect to uncertainties in the parameters of the epidemiological model and only requires measurements of the number of individuals who require medical attention. Therefore, it may serve as a first step towards a reliable decision makin…
Leveraging recent developments in black-box risk-aware verification, we provide three algorithms that generate probabilistic guarantees on (1) optimality of solutions, (2) recursive feasibility, and (3) maximum controller runtimes for general nonlinear safety-critical finite-time optimal controllers. These methods forego the usual (perhaps) restrictive assumptions required for typical theoretical guarantees, e.g. terminal set calculation for recursive feasibility in Nonlinear Model Predictive Control, or convexification of optimal controllers to ensure optimality. Furthermore, we show that the…
We consider the decentralized control of a discrete-time, linear system subject to exogenous disturbances and polyhedral constraints on the state and input trajectories. The underlying system is composed of a finite collection of dynamically coupled subsystems, where each subsystem is assumed to have a dedicated local controller. The decentralization of information is expressed according to sparsity constraints on the state measurements that each local controller has access to. In this context, we investigate the design of decentralized controllers that are affinely parameterized in their meas…
Finite-dimensional observer-based controller design for PDEs is a challenging problem. Recently, such controllers were introduced for the 1D heat equation, under the assumption that one of the observation or control operators is bounded. This paper suggests a constructive method for such controllers for 1D parabolic PDEs with both (observation and control) operators being unbounded. We consider the Kuramoto-Sivashinsky equation (KSE) under either boundary or in-domain point measurement and boundary actuation. We employ a modal decomposition approach via dynamic extension, using eigenfunctions …
This paper considers online switching control with a finite candidate controller pool, an unknown dynamical system, and unknown cost functions. The candidate controllers can be unstabilizing policies. We only require at least one candidate controller to satisfy certain stability properties, but we do not know which one is stabilizing. We design an online algorithm that guarantees finite-gain stability throughout the duration of its execution. We also provide a sublinear policy regret guarantee compared with the optimal stabilizing candidate controller. Lastly, we numerically test our algorithm…
In this work, we investigate the problem of simultaneously learning and controlling a system subject to adversarial choices of disturbances and system parameters. We study the problem for a scalar system with $l_\infty$-norm bounded disturbances and system parameters constrained to lie in a known bounded convex polytope. We present a controller that is globally stabilizing and gives continuously improving bounds on the worst-case state deviation. The proposed controller simultaneously learns the system parameters and controls the system. The controller emerges naturally from an optimization pr…
We propose a tube-based guaranteed cost model predictive controller considering a homothetic formulation for constrained linear systems subject to multiplicative structured norm-bounded uncertainties. It provides an upper bound to the general min-max model predictive control. The invariance property of the proposed tube holds for any arbitrary scaling. It yields a second-order cone programming problem which is less computationally expensive than standard semi-definite programming problems. We also present a numerical example with a comparative study among the proposed approach, an open-loop gu…
A suboptimal active disturbance rejection controller (S-ADRC) is proposed for second-order systems with unknown time-varying nonlinear dynamics. The output-feedback controller guarantees a global convergence to the vicinity of an optimal solution by means of dynamic control gains, based on the estimated main and extended state variables obtained through a high-gain observer. Three numerical examples compare the performance of the proposed control scheme applied to linear and nonlinear systems with that of a fixed-gain conventional ADRC as well as several model-based optimal and suboptimal cont…
We address the problem of simultaneously learning and control in an online receding horizon control setting. We consider the control of an unknown linear dynamical system with general cost functions and affine constraints on the control input. Our goal is to develop an online learning algorithm that minimizes the dynamic regret, which is defined as the difference between the cumulative cost incurred by the algorithm and that of the best policy with full knowledge of the system, cost functions and state and that satisfies the control input constraints. We propose a novel approach to explore in …
Negative Imaginary Neural ODEs: Learning to Control Mechanical Systems with Stability Guarantees
Australian Centre for Robotics and School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney（澳大利亚机器人中心和航空航天、机械与机电工程学院，悉尼大学）
Neural networks can be used as approximations of several complex control schemes such as model predictive control. We show in this paper which properties deep neural networks with rectifier linear units as activation functions need to satisfy to guarantee constraint satisfaction and asymptotic stability of the closed-loop system. To do so, we introduce a parametric description of the neural network controller and use a mixed-integer linear programming formulation to perform output range analysis of neural networks. We also propose a novel method to modify a neural network controller such that …
In this work we consider the online control of a known linear dynamic system with adversarial disturbance and adversarial controller cost. The goal in online control is to minimize the regret, defined as the difference between cumulative cost over a period $T$ and the cumulative cost for the best policy from a comparator class. For the setting we consider, we generalize the previously proposed online Disturbance Response Controller (DRC) to the adaptive gradient online Disturbance Response Controller. Using the modified controller, we present novel regret guarantees that improves the establish…
University of California, Berkeley（加州大学伯克利分校）；University of Pennsylvania（宾夕法尼亚大学）
In this work, we propose a robust approach to design distributed controllers for unknown-but-sparse linear and time-invariant systems. By leveraging modern techniques in distributed controller synthesis and structured linear inverse problems as applied to system identification, we show that near-optimal distributed controllers can be learned with sub-linear sample complexity and computed with near-linear time complexity, both measured with respect to the dimension of the system. In particular, we provide sharp end-to-end guarantees on the stability and the performance of the designed distribut…
We study the control of an \emph{unknown} linear dynamical system under general convex costs. The objective is minimizing regret vs. the class of disturbance-feedback-controllers, which encompasses all stabilizing linear-dynamical-controllers. In this work, we first consider the case of known cost functions, for which we design the first polynomial-time algorithm with $n^3\sqrt{T}$-regret, where $n$ is the dimension of the state plus the dimension of control input. The $\sqrt{T}$-horizon dependence is optimal, and improves upon the previous best known bound of $T^{2/3}$. The main component of …
Reinforcement learning (RL) in the context of control systems offers wide possibilities of controller adaptation. Given an infinite-horizon cost function, the so-called critic of RL approximates it with a neural net and sends this information to the controller (called "actor"). However, the issue of closed-loop stability under an RL-method is still not fully addressed. Since the critic delivers merely an approximation to the value function of the corresponding infinite-horizon problem, no guarantee can be given in general as to whether the actor's actions stabilize the system. Different approa…
The paper deals with the design of nonlinear adaptive cruise controllers for vehicular platoons operating on an open road or a ring-road. The constructed feedback controllers are nonlinear functions of the distance between successive vehicles and their speeds. It is shown that the proposed novel controllers guarantee safety (collision avoidance) and bounded vehicle speeds by explicitly characterizing the set of allowable inputs. Moreover, we guarantee global asymptotic stability of the platoon to a desired configuration as well as string stability. Certain macroscopic properties are also inves…
This paper considers the linear-quadratic dual control problem where the system parameters need to be identified and the control objective needs to be optimized in the meantime. Contrary to existing works on data-driven linear-quadratic regulation, which typically provide error or regret bounds within a certain probability, we propose an online algorithm that guarantees the asymptotic optimality of the controller in the almost sure sense. Our dual control strategy consists of two parts: a switched controller with time-decaying exploration noise and Markov parameter inference based on the cross…
University of California, Berkeley（加州大学伯克利分校）；California Institute of Technology（加州理工学院）
Modern nonlinear control theory seeks to develop feedback controllers that endow systems with properties such as safety and stability. The guarantees ensured by these controllers often rely on accurate estimates of the system state for determining control actions. In practice, measurement model uncertainty can lead to error in state estimates that degrades these guarantees. In this paper, we seek to unify techniques from control theory and machine learning to synthesize controllers that achieve safety in the presence of measurement model uncertainty. We define the notion of a Measurement-Robus…
In this paper we propose a novel decision making architecture for Robust Model Predictive Path Integral control (RMPPI) and investigate its performance guarantees and applicability to off-road navigation. Key building blocks of the proposed architecture are an augmented state space representation of the system consisting of nominal and actual dynamics, a placeholder for different types of tracking controllers, a safety logic for nominal state propagation, and an importance sampling scheme that takes into account the capabilities of the underlying tracking control. Using these ingredients, we d…
The weight, space, and power limitations of small aerial vehicles often prevent the application of modern control techniques without significant model simplifications. Moreover, high-speed agile behavior, such as that exhibited in drone racing, make these simplified models too unreliable for safety-critical control. In this work, we introduce the concept of time-varying backup controllers (TBCs): user-specified maneuvers combined with backup controllers that generate reference trajectories which guarantee the safety of nonlinear systems. TBCs reduce conservatism when compared to traditional ba…
Engineered cyberphysical systems are growing increasingly large and complex. These systems require scalable controllers that robustly satisfy state and input constraints in the presence of additive noise -- such controllers should also be accompanied by theoretical guarantees on feasibility and stability. In our companion paper, we introduced Distributed and Localized Model Predictive Control (DLMPC) for large-scale linear systems; DLMPC is a scalable closed-loop MPC scheme in which subsystems need only exchange local information in order to synthesize and implement local controllers. In this …
Sydney Institute for Robotics and Intelligent Systems（悉尼机器人与智能系统研究所）；Australian Centre for Field Robotics（澳大利亚野外机器人中心）；School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney（悉尼大学航空航天、机械与机电工程学院）
This paper proposes a nonlinear policy architecture for control of partially-observed linear dynamical systems providing built-in closed-loop stability guarantees. The policy is based on a nonlinear version of the Youla parameterization, and augments a known stabilizing linear controller with a nonlinear operator from a recently developed class of dynamic neural network models called the recurrent equilibrium network (REN). We prove that RENs are universal approximators of contracting and Lipschitz nonlinear systems, and subsequently show that the the proposed Youla-REN architecture is a unive…
University of California, Santa Cruz（加州大学圣克鲁兹分校）；NASA Langley Research Center（美国国家航空航天局兰利研究中心）；Naval Postgraduate School（海军研究生院）
Recent research shows that supervised learning can be an effective tool for designing near-optimal feedback controllers for high-dimensional nonlinear dynamic systems. But the behavior of neural network controllers is still not well understood. In particular, some neural networks with high test accuracy can fail to even locally stabilize the dynamic system. To address this challenge we propose several novel neural network architectures, which we show guarantee local asymptotic stability while retaining the approximation capacity to learn the optimal feedback policy semi-globally. The proposed …
