Valery A. Ugrinovskii

Distributed robust filtering with H ∞ consensus of estimates

The paper addresses a problem of design of distributed robust filters using the recent vector dissipativity theory. The main result is a sufficient condition which guarantees a suboptimal H ∞ level of disagreement of estimates in a network of filters. It involves solving a convex optimization/feasibility problem subject to LMI constraints. The special case of balanced interconnection graphs is also considered. A gradient descent type algorithm is presented which allows the nodes to compute their estimator parameters in a decentralized manner. The proposed approach is applied to the problem of observer-based robust synchronization of a nonlinear network to an isolated node.

Robust H∞ infinity control in the presence of stochastic uncertainty

This paper considers a robust H infinity state feedback control problem for linear uncertain systems with stochastic uncertainty. The uncertainty class considered in the paper involves uncertain multiplicative white noise perturbations which satisfy a certain variance constraint. A state feedback controller is presented which guarantees a prescribed level of disturbance attenuation for all admissible stochastic uncertainties.

Decentralized robust control of uncertain Markov jump parameter systems via output feedback

We address the problem of decentralized robust control of uncertain Markov jump parameter systems via output feedback, which extends recent results on decentralized state feedback control. It is shown that the feasibility of a parametrized collection of mode-dependent coupled algebraic Riccati equations and inequalities are both sufficient and necessary for the existence of a robust decentralized switching controller. A guaranteed upper bound on robust performance is also obtained

On Necessary and Sufficient Conditions for

This note addresses the output feedback Hinfin control problem for continuous-time Markov jump linear systems. It is shown that the feasibility of a certain set of linear matrix inequalities is both sufficient and necessary for the existence of a solution. Under standard assumptions, we also give a Riccati-type sufficient and necessary condition for an Hinfin-suboptimal controller to exist.

{H}_{\infty }

Abstract. We consider a linear-quadratic problem of minimax optimal control for stochastic uncertain control systems with output measurement. The uncertainty in the system satisfies a stochastic integral quadratic constraint. To convert the constrained optimization problem into an unconstrained one, a special S-procedure is applied. The resulting unconstrained game-type optimization problem is then converted into a risk-sensitive stochastic control problem with an exponential-of-integral cost functional. This is achieved via a certain duality relation between stochastic dynamic games and risk-sensitive stochastic control. The solution of the risk-sensitive stochastic control problem in terms of a pair of differential matrix Riccati equations is then used to establish a minimax optimal control law for the original uncertain system with uncertainty subject to the stochastic integral quadratic constraint.

Output Feedback Control of Markov Jump Linear Systems

This paper is concerned with existence and optimality properties of so-called guaranteed cost controllers for an uncertain system subject to structured uncertainty. The uncertainty in the system is assumed to have a stochastic character and to satisfy certain stochastic integral constraints. It is shown that a minimax optimal guaranteed cost state feedback controller for a stochastic system can be synthesized as a state feedback controller absolutely stabilizing this system. For each initial state of the system, this controller can be found by parametric optimization of solutions of a parameter-dependent generalized matrix Riccati equation arising in stochastic

Finite Horizon Minimax Optimal Control of Stochastic Partially Observed Time Varying Uncertain Systems

H_\infty

Absolute Stabilization and Minimax Optimal Control of Uncertain Systems with Stochastic Uncertainty

theory.

Minimax LQG Control of Stochastic Partially Observed Uncertain Systems

We consider an infinite-horizon linear-quadratic minimax optimal control problem for stochastic uncertain systems with output measurement. A new description of stochastic uncertainty is introduced using a relative entropy constraint. For the stochastic uncertain system under consideration, a connection between the worst-case control design problem and a specially parametrized risk-sensitive stochastic control problem is established. Using this connection, a minimax optimal LQG controller is constructed which is based on a pair of algebraic matrix Riccati equations arising in risk-sensitive control. It is shown that this minimax optimal controller absolutely stabilizes the stochastic uncertain system.

Decentralized state-feedback stabilization and robust control of uncertain large-scale systems with integrally constrained interconnections☆

Abstract This paper is concerned with a problem of stabilization and robust control design for interconnected uncertain systems. A new class of uncertain large-scale systems is considered in which interconnections between subsystems as well as uncertainties in each subsystem are described by integral quadratic constraints. The problem is to design a set of local (decentralized) controllers which stabilize the overall system and guarantee robust disturbance attenuation in the presence of the uncertainty in interconnections between subsystems as well as in each subsystem. The paper presents necessary and sufficient conditions for the existence of such a controller. The proposed design is based on recent absolute stabilization and minimax optimal control results and employs solutions of a set of game-type Riccati algebraic equations arising in H ∞ control.