A Small-Gain Theorem, which can be applied to a wide class of systems that includes systems satisfying the weak semigroup property, is presented in the present work. The result generalizes all existing results in the literature and exploits notions of weighted, uniform and non-uniform Input-to-Output Stability (IOS) property. Applications to partial state feedback stabilization problems with sampled-data feedback applied with zero order hold and positive sampling rate, are also presented.
New trajectory-based small-gain results are obtained for nonlinear feedback systems under relaxed assumptions. Specifically, during a transient period, the solutions of the feedback system may not satisfy some key inequalities that previous small-gain results usually utilize to prove stability properties. The results allow the application of the small-gain perspective to various systems which satisfy less demanding stability notions than the Input-to-Output Stability property. The robust global feedback stabilization problem of an uncertain time-delayed chemostat model is solved by means of th…
We propose a new matrix pencil based approach for design of state-feedback and output-feedback stabilizing controllers for a general class of uncertain nonlinear strict-feedback-like systems. While the dynamic controller structure is based on the dual dynamic high-gain scaling based approach, we cast the design procedure within a general matrix pencil structure unlike prior results that utilized conservative algebraic bounds of terms arising in Lyapunov inequalities. The design freedoms in the dynamic controller are extracted in terms of generalized eigenvalues associated with matrix pencils f…
A learning approach for optimal feedback gains for nonlinear continuous time control systems is proposed and analysed. The goal is to establish a rigorous framework for computing approximating optimal feedback gains using neural networks. The approach rests on two main ingredients. First, an optimal control formulation involving an ensemble of trajectories with 'control' variables given by the feedback gain functions. Second, an approximation to the feedback functions via realizations of neural networks. Based on universal approximation properties we prove the existence and convergence of opti…
Firstly, a new state feedback model reference adaptive control approach is developed for uncertain systems with gain scheduled reference models in a multi-input multi-output (MIMO) setting. Specifically, adaptive state feedback for output tracking control problem of MIMO nonlinear systems is studied and gain scheduled reference model system is used for generating desired state trajectories. Using convex optimization tools, a common Lyapunov matrix is computed for multiple linearizations near equilibrium and non-equilibrium points of the nonlinear closed loop gain scheduled reference system. Th…
In the present work a new controller called Particle Swarm Optimization based state feedback gain controller has been proposed for frequency regulation of a two area system and then its performance is compared with earlier designed controllers such as Linear Quadratic Regulator Proportional Integral controller and Integral controller. The performance comparison has been done for the power system network comprising of two thermal power plants which are tie line connected. For using the optimal control based method such as LQR PI controller and computationally intelligent method such as PSO base…
Motivated by improving performance of a bi-stable vibration energy harvester (VEH) from the viewpoint of vibration control, the time-delayed feedback control of displacement and velocity are constructively proposed into an electromechanical coupled VEH mounted on a rotational automobile tire, which is subject to colored noise and the periodic excitation. Using the improved stochastic averaging procedure based on energy-dependent frequency, the expressions of stationary probability density (SPD) and signal-to-noise ratio (SNR) are obtained analytically. Then, the efficiency of time-delayed feed…
This paper analyzes output feedback control of a class of unknown nonlinear systems in the presence of measurement noise using multiple high-gain observers (MHGO). It is well-known that single high-gain observers (HGO) are not able to provide satisfactory performance when the system output is contaminated by noise. More specifically, there is a trade-off between the convergence speed of state estimation and the bound of steady estimation error in HGO when the output measurement is contaminated by noise. In the presented scheme, the output feedback controller utilizes the state estimation obtai…
In this paper we demonstrate how certain structured feedback gains necessarily emerge as the optimal controller gains in two linear optimal control formulations for multi-agent systems. We consider the cases of linear optimal synchronization and linear optimal centroid stabilization. In the former problem, the considered cost functional integrates squared synchronization error and input, and in the latter, the considered cost functional integrates squared sum of the states and input. Our approach is to view the structures in the feedback gains in terms of a static output feedback with suitable…
This paper considers linear discrete-time systems with additive disturbances, and designs a Model Predictive Control (MPC) law incorporating a dynamic feedback gain to minimise a quadratic cost function subject to a single chance constraint. The feedback gain is selected online and we provide two selection methods based on minimising upper bounds on predicted costs. The chance constraint is defined as a discounted sum of violation probabilities on an infinite horizon. By penalising violation probabilities close to the initial time and assigning violation probabilities in the far future with va…
Infinite-dimensional linear systems with unbounded input and output operators are considered. For the purpose of finite-dimensional observer-based state feedback, an observer approximation scheme will be developed which can be directly combined with existing late-lumping controllers and observer output injection gains. It relies on a decomposition of the feedback gain, resp. observer output injection gain, into a bounded and an unbounded part. Based on a perturbation result, the spectrum-determined growth condition is established, for the closed loop.
The minimum-gain eigenvalue assignment/pole placement problem (MGEAP) is a classical problem in LTI systems with static state feedback. In this paper, we study the MGEAP when the state feedback has arbitrary sparsity constraints. We formulate the sparse MGEAP problem as an equality-constrained optimization problem and present an analytical characterization of its locally optimal solution in terms of eigenvector matrices of the closed loop system. This result is used to provide a geometric interpretation of the solution of the non-sparse MGEAP, thereby providing additional insights for this cla…
We derive gain-tuning rules for the positive and negative spatial-feedback loops of a spatially-distributed filter to change the resolution of its spatial band-pass characteristic accordingly to a wavelet zoom, while preserving temporal stability. The filter design is inspired by the canonical spatial feedback structure of the primary visual cortex and is motivated by understanding attentional control of visual resolution. Besides biology, our control-theoretical design strategy is relevant for the development of neuromorphic multiresolution distributed sensors through the feedback interconnec…
We propose a deep unfolding-based approach for stabilization of time-delay linear systems. Deep unfolding is an emerging framework for design and improvement of iterative algorithms and attracting significant attentions in signal processing. In this paper, we propose an algorithm to design a static output feedback gain for stabilizing time-delay linear systems via deep unfolding. Within the algorithm, the learning part is driven by NeuralODE developed in the community of machine learning, while the gain verification is performed with linear matrix inequalities developed in the systems and cont…
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…
Memory Resilient Gain-scheduled State-Feedback Control of Uncertain LTI/LPV Systems with Time-Varying Delays
KTH, School of Mathematics（瑞典皇家理工学院数学学院）；GIPSA-Lab, Departement of Control Systems (former LAG), Grenoble Universités, ENSE 3（格勒诺布尔大学 GIPSA 实验室控制系统系（原 LAG））；IRCCyN - Centrale de Nantes（南特中央理工学院 IRCCyN）
Load frequency control (LFC) is a key factor to maintain the stable frequency in multi-area power systems. As the modern power systems evolve from centralized to distributed paradigm, LFC needs to consider the peer-to-peer (P2P) based scheme that considers limited information from the information-exchange graph for the generator control of each interconnected area. This paper aims to solve a data-driven constrained LQR problem with mean-variance risk constraints and output structured feedback, and applies this framework to solve the LFC problem in multi-area power systems. By reformulating the…
This paper deals with suboptimal distributed H2 control by dynamic output feedback for homogeneous linear multi-agent systems. Given a linear multi-agent system, together with an associated H2 cost functional, the objective is to design dynamic output feedback protocols that guarantee the associated cost to be smaller than an a priori given upper bound while synchronizing the controlled network. A design method is provided to compute such protocols. The computation of the two local gains in these protocols involves two Riccati inequalities, each of dimension equal to the dimension of the state…
The usual passivity theorem considers a closed-loop, the direct chain of which consists of a strictly passive stable operator $H_{1}$, and the feedback chain of which consists of a passive operator $H_{2}$. Then the closed-loop is stable. Let $ρ>1$. We show here that the closed-loop is still stable when the direct chain consists of a strictly $ρ^{-1}$-passive $% ρ^{-1}$-stable operator (a weaker condition than above) and the feedback chain consists of a $ρ$-passive operator (a stronger condition than above). Variations on the theme of the small gain theorem (incremental or not) can be made sim…
Error Estimates of the Gain Approximation by Hermite-Galerkin Method in Feedback Particle Filter
School of Mathematical Sciences, Beihang University（北京航空航天大学数学科学学院）；Key Laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University（北京航空航天大学数学、信息与行为语义重点实验室）
In this work, we revisit the Linear Quadratic Gaussian (LQG) optimal control problem from a behavioral perspective. Motivated by the suitability of behavioral models for data-driven control, we begin with a reformulation of the LQG problem in the space of input-output behaviors and obtain a complete characterization of the optimal solutions. In particular, we show that the optimal LQG controller can be expressed as a static behavioral-feedback gain, thereby eliminating the need for dynamic state estimation characteristic of state space methods. The static form of the optimal LQG gain also make…
Texas A\&M University, College Station TX 77843, USA, .
We consider the problem of robotic planning under uncertainty. This problem may be posed as a stochastic optimal control problem, complete solution to which is fundamentally intractable owing to the infamous curse of dimensionality. We report the results of an extensive simulation study in which we have compared two methods, both of which aim to salvage tractability by using alternative, albeit inexact, means for treating feedback. The first is a recently proposed method based on a near-optimal "decoupling principle" for tractable feedback design, wherein a nominal open-loop problem is solved,…
