Showing papers by "Ian R. Petersen published in 1998"
TL;DR: The main result is a recursive scheme for constructing an ellipsoidal state estimation set of all states consistent with the measured output and the given noise and uncertainty description.
143 citations
TL;DR: The problem of constructing a controller which quadratically stabilizes an uncertain system and minimizes a guaranteed cost bound on a quadratic cost function is considered and the solution is obtained via a parameter-dependent linear matrix inequality problem.
Abstract: This paper considers the problem of constructing a controller which quadratically stabilizes an uncertain system and minimizes a guaranteed cost bound on a quadratic cost function. The solution is obtained via a parameter-dependent linear matrix inequality problem. © 1998 John Wiley & Sons, Ltd.
109 citations
16 Dec 1998
TL;DR: In this article, the authors give a stochastic small gain theorem for risk-sensitive control with deterministic H/sub /spl infin// control and show that the risk sensitive controller is robust.
Abstract: It is well-known that there are strong connections between risk-sensitive stochastic control and deterministic H/sub /spl infin// control. These connections have stimulated interest in the risk-sensitive control problem. But is the risk-sensitive controller robust? This paper answers this question in an affirmative and precise way, and gives a stochastic small gain theorem and a stochastic robust stability result.
86 citations
01 Nov 1998
TL;DR: In this paper, the feasibility of a linear matrix inequality (LMI) problem is proved for the quadratic stabilisation of an uncertain time-delay system with norm bounded uncertainty, and a robust state feedback controller can be constructed using the corresponding feasible solution of the LMI problem.
Abstract: Results on the design of robust memoryless state feedback controllers for uncertain time-delay systems with norm bounded uncertainty are presented. It is proved that the feasibility of a linear matrix inequality (LMI) problem is necessary and sufficient for the quadratic stabilisation of an uncertain time-delay system. A robust state feedback controller can be constructed using the corresponding feasible solution of the LMI problem. A procedure is given to select a suitable state feedback controller that is also suboptimal in the sense of minimising a bound on a quadratic performance index.
67 citations
TL;DR: In this paper, the problems of robust filtering, robust prediction, and robust smoothing for a class of continuous time uncertain systems are defined, and non-conservative solutions are given in terms of Riccati differential equations.
Abstract: This paper is concerned with a class of continuous time uncertain systems which satisfy a certain Integral Quadratic Constraint. The problems of robust filtering, robust prediction, and robust smoothing for such systems are defined, and nonconservative solutions are given in terms of Riccati differential equations. This paper also addresses a problem of robust observability for this class of uncertain systems.
65 citations
TL;DR: A set-valued state estimate is obtained by solving a Hamilton-Jacobi-Bellman equation that leads to a robust version of the extended Kalman filter.
Abstract: This paper considers a problem of robust filtering for a class of uncertain nonlinear systems. The solution involves a set-valued state estimate that is obtained by solving a Hamilton-Jacobi-Bellman equation. In addition, a less computationally intensive approximate solution to the problem is obtained for filtering problems defined over a large time interval. The paper also presents an approximate solution to the robust filtering problem, which leads to a robust version of the extended Kalman filter.
60 citations
21 Jun 1998
TL;DR: In this paper, the authors considered a class of uncertain large-scale systems in which interconnections between subsystems as well as uncertainties in each subsystem are described by integral quadratic constraints.
Abstract: This paper is concerned with a problem of stabilization and robust control design for interconnected uncertain systems. The 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/sub /spl infin// control.
46 citations
16 Dec 1998
TL;DR: In this article, the authors considered the problem of output-feedback guaranteed cost controller design for uncertain time-delay systems, where the uncertainty in the system is assumed to be norm-bounded and time-varying.
Abstract: This paper considers the problem of output-feedback guaranteed cost controller design for uncertain time-delay systems The uncertainty in the system is assumed to be norm-bounded and time-varying. The time-delay is allowed to enter the state and the measurement equations. It is proved that the existence of the guaranteed cost controller is equivalent to the feasibility of certain matrix inequalities. A numerical algorithm is developed to construct a full order output-feedback controller that minimizes a specific cost bound for a quadratic performance index.
35 citations
01 Jan 1998
30 citations
TL;DR: This paper is concerned with the problem of designing guaranteed cost controllers for a class of norm bounded uncertain systems with a time multiplied linear quadratic cost function that penalizes the states heavily as time increases, and hence, forces the states to approach zero more quickly.
25 citations
16 Dec 1998
TL;DR: In this paper, the application of piezoelectric materials in active control of unwanted vibrations in flexible structures using spatial control is discussed, and two new controller design methodologies, spatial LQG control and spatial H/sub /spl infin// control are presented.
Abstract: This paper deals with the application of piezoelectric materials in active control of unwanted vibrations in flexible structures using spatial control. Two new controller design methodologies, spatial LQG control and spatial H/sub /spl infin// control are presented in the paper. Some experimental results are also included.
21 Jun 1998
TL;DR: In this paper, a new formulation of the acoustic noise and vibration control problem for flexible structures is presented, where the problem is formulated as a spatial control problem, e.g., acoustic noise in an entire duct, i.e., distributed over the entire physical space of the duct, should be reduced.
Abstract: This paper presents a new formulation of the acoustic noise and vibration control problem for flexible structures. The problem is formulated as a spatial control problem, e.g., acoustic noise in an entire duct, i.e., distributed over the entire physical space of the duct, should be reduced. In the paper it is shown that for certain configurations it is possible to solve this spatial control problem by reducing it to the standard linear quadratic Gaussian (LQG) or the H/sub /spl infin// problem.
TL;DR: The main result of the paper presents a scheme for constructing a collection of decentralized controllers which stabilizes the system and is optimal with respect to a quadratic performance index.
Abstract: Presents an approach to the optimal stabilization of a linear time-invariant system via decentralized control. The class of controllers considered does not restrict the controller to be finite dimensional or time invariant. In fact, the controller structure proposed can be regarded as a form of time varying sampled data control. The main result of the paper presents a scheme for constructing a collection of decentralized controllers which stabilizes the system and is optimal with respect to a quadratic performance index.
16 Dec 1998
TL;DR: In this paper, the authors considered a linear-quadratic infinite-horizon time-averaged guaranteed cost control problem for stochastic uncertain systems with output measurement, where a new class of uncertainty is introduced that satisfies a stochastically relative entropy constraint.
Abstract: We consider a linear-quadratic infinite-horizon time-averaged guaranteed cost control problem for stochastic uncertain systems with output measurement. A new class of uncertainty is introduced that satisfies a stochastic relative entropy constraint. The solution of a specially parametrized risk-sensitive stochastic control problem based on a pair of algebraic matrix Riccati equations is used to establish a guaranteed cost control law for the original uncertain system. It is shown that this guaranteed cost control absolutely stabilizes the system.
TL;DR: It is shown that for the existence of such a controller, it is sufficient that the plant be stabilizable and detectable and the control law is required to be almost optimal with respect to a quadratic performance index.
TL;DR: In this article, an approach to the problems of robust filtering and model validation for a class of continuous time uncertain systems with both discrete-time and continuous-time measured outputs is presented.
Abstract: An approach to the problems of robust filtering and model validation for a class of continuous-time uncertain systems with both discrete-time and continuous-time measured outputs is presented. The uncertainty description being considered is a generalization of the integral quadratic constraint uncertainty description. The proposed algorithm is based on the solution to a jump Riccati differential equation and a set of jump state equations. In these jump equations, the solutions exhibit finite jumps at the measurement sampling instants. The equations in our robust filtering and model validation algorithm are closely related to those in the Kalman filtering problem.
TL;DR: In this article, the authors apply a nonlinear S-procedure result on nonlinear H∞-optimal control to give a necessary and sufficient condition for the existence of a state feedback controller which absolutely stabilizes a discrete-time uncertain nonlinear system with structured uncertainty.
Abstract: This paper applies a recent result on nonlinear H∞-optimal control to give a necessary and sufficient condition for the existence of a state feedback controller which absolutely stabilizes a discrete-time uncertain nonlinear system with structured uncertainty. The class of uncertain systems being considered contain uncertainties which satisfy a certain sum constraint. This sum constraint is a nonlinear discrete-time version of the integral quadratic constraint uncertainty description. The main result is established by using a nonlinear S-procedure result, which enables the robust absolute stabilization problem to be converted into a equivalent nonlinear H∞-optimal control problem.
21 Jun 1998
TL;DR: In this paper, the authors apply a result on output feedback guaranteed cost control of stochastic uncertain systems to the problem of designing a missile autopilot, where the given data is a finite collection of plant models for the missile corresponding to different flight conditions.
Abstract: We apply a result on output feedback guaranteed cost control of stochastic uncertain systems to the problem of designing a missile autopilot. In the missile autopilot design problem, the given data is a finite collection of plant models for the missile corresponding to different flight conditions. A total least squares approach is used to fit the data to a norm bounded uncertain system model.