Robust output feedback control for linear stochastic systems in continuous time with time-varying parameters

This paper proposes guaranteed cost design of robust output feedback controller for continuous linear parametric uncertain systems. New necessary and sufficient conditions for static output feedback stabilizability of linear continuous time systems underly the design procedure. Proposed algorithms are computationally simple and tightly connected with the Lyapunov stability theory and the LQR optimal state feedback design. The proposed approach allows for prescribing the structure of the output feedback gain matrix (including the decentralized one) by the designer. New design method proposed in this paper, exploit genetic algorithm to design robust controller with guaranteed cost for polytopic linear continuous time systems. Numerical example is given to illustrate the performance of the proposed robust controller.

A vector decomposition approach to F–M model realization and its application to robust observed-state feedback control

This article deals with the problem of optimal static output feedback control of linear periodic systems in continuous time, for which a continuous-time approach, which allows to deal with both stable and unstable open loop systems, is presented. The proposed approach is tested on the problem of designing attitude control laws for a Low-Earth Orbit (LEO) satellite on the basis of feedback from a triaxial magnetometer and a set of high-precision gyros. Simulation results are used to demonstrate the feasibility of the proposed strategy and to evaluate its performance.

The aim of this presentation is to construct a robust optimal PID feedback controller, taking into account stochastic uncertainties in the initial conditions. Usually, a precomputed feedback control is based on exactly known model parameters. However, in practice, often exact information about model parameters and initial values is not given. Hence, having an inital point, which differs from the nominal values, a standard precomputed controller may produce bad results. Supposing now that the probability distribution of the random parameter variations is known, in the following stochastic optimisation methods will be applied in order to obtain robust optimal feedback controls. Taking into account stochastic parameter variations at the initial point, the method works with expected total costs arising from the primary control expenses and the tracking error. Furthermore, the free regulator parameters are selected then such that the expected total costs are minimized. After Taylor expansion to calculate expected cost functions and a few transformations an approximate deterministic substitute control problem follows. Here, retaining only linear terms, approximation of expectations and variances of the expected cost functions can be calculated explicitly. By means of splines, numerical approximations of the objective function and the differential equations are obtained then. Using stochastic optimization methods, random parameter variations are incorporated into the optimal control process. Hence, robust optimal feedback controls are obtained. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

This chapter studies null controllability of continuous-time linear systems with bounded controls. Null controllability of a system refers to the possibility of steering its state to the origin in a finite time by an appropriate choice of the admissible control input. If the system is linear and is controllable, then any state can be steered to any other location, for example, the origin, in the state space in a finite time by a control input. This implies that any controllable linear system is null controllable from any point in the state space. The control inputs that are used to drive certain states to the origin, however, might have to be large in magnitude. As a result, when the control input is limited by the actuator saturation, a linear controllable system might not be globally null controllable. In this situation, it is important to identify the set of all the states that can be steered to the origin with the bounded controls delivered by the actuators. This set is referred to as the null controllable region and is denoted as C

The equivalent representation in the delta domain of the digital optimal compensation problem is provided and computed in this article. This problem concerns finding digital optimal full and reduced-order output feedback controllers for linear time-varying and time-invariant systems with white stochastic parameters. It can subsequently be solved in the delta domain using the strengthened optimal projection equations that we recently formulated in this domain as well. If the sampling rate becomes high, stating and solving the problem in the delta domain becomes necessary because the conventional discrete-time problem formulation and solution become ill-conditioned. In this article, by means of several numerical examples and compensator implementations, we demonstrate this phenomenon. To compute and quantify the improved performance when the sampling rate becomes high, a new delta-domain algorithm is developed. This algorithm computes the performance of arbitrary digital compensators for linear systems with white stochastic parameters. The principle application concerns nonconservative robust digital perturbation feedback control of nonlinear systems with high sampling rates.

For discrete-time uncertain linear systems with constraints on inputs and states, we develop an approach to determine state feedback controllers based on a min-max control formulation. Robustness is achieved against additive norm-bounded input disturbances and/or polyhedral parametric uncertainties in the state-space matrices. We show that the finite-horizon robust optimal control law is a continuous piecewise affine function of the state vector and can be calculated by solving a sequence of multiparametric linear programs. When the optimal control law is implemented in a receding horizon scheme, only a piecewise affine function needs to be evaluated on line at each time step. The technique computes the robust optimal feedback controller for a rather general class of systems with modest computational effort without needing to resort to gridding of the state-space.

On the quasi-decentralized estimation and control of linear stochastic systems

First, a review of some recent developments in stochastic adaptive control of linear stochastic systems is given. By integrating and refining several basic ideas in these developments, a relatively complete asymptotic solution to the adaptive control problem is then provided for such systems. The solution involves parallel implementation of a few basic recursive identification algorithms that serve to complement each other. It also involves occasional use of a dither signal to probe the system for information.

SUMMARY The LQ+ problem, i.e. the finite-horizon linear quadratic optimal control problem with nonnegative state constraints, is studied for positive linear systems in continuous time and in discrete time. Necessary and sufficient optimality conditions are obtained by using the maximum principle. These conditions lead to a computational method for the solution of the LQ+ problem by means of a corresponding Hamiltonian system. In addition, the necessary and sufficient conditions are proved for the LQ+-optimal control to be given by the standard LQ-optimal state feedback law. Then sufficient conditions are established for the positivity of the LQ-optimal closed-loop system. In particular, such conditions are obtained for the problem of minimal energy control with penalization of the final state. Moreover, a positivity criterion for the LQ-optimal closed-loop system is derived for positive discrete-time systems with a positively invertible (dynamics) generator. The main results are illustrated by numerical examples. Copyright q 2010 John Wiley & Sons, Ltd.

In this paper, we study the robust output feedback control for a class of time-varying systems where the observer is used to estimate the system states and a learning scheme is also proposed to learn the time-varying parameters. A regulator control problem is pursued with known time-varying bounds. It is shown that to estimate the system states asymptotically only part of the time-varying function need to be learned, not necessarily all the time-varying parameters. The designed output feedback closed-loop control system guarantees a robust norm bound performance measure and uniformly asymptotic stability based on quadratic stability.

The deployment of Autonomous Underwater Vehicles (AUVs) for ocean observation is one of the important methods in marine scientific research. The stability of AUV attitude control determines the efficiency and safety of underwater operations. In practical systems, the actuators carried by AUVs have saturation, and the saturation of the actuators greatly affects the performance and stability of AUV attitude control. This article designs an anti-windup [Formula: see text] robust state feedback controller and an anti-windup [Formula: see text] robust dynamic output feedback controller for the pitch attitude control of AUVs to solve the pitch attitude control problem of AUVs subject to input constraints. Firstly, building a Linear-parameter varying (LPV) model for the AUV. Then, we design two anti-windup [Formula: see text] robust controllers based on LPV model. Simulation results verify the reasonable of LPV model and the effectiveness of proposed controllers. Proposed controllers can enable the system to quickly reach the desired attitude under input constraints.

Constrained Feedback Control of Imperfectly Known, Linear, Time-Delay Systems of Neutral Type

A robust dynamic output feedback controller synthesis algorithm considering H∞/H2performance and regional pole placement is addressed for a nonlinear system with parameter uncertainties and external disturbance. First, the formulation of a gain‐scheduled mixed‐objective robust dynamic output feedback controller for continuous‐time polytopic linear parameter varying (LPV) systems is presented. To reduce conservativeness, some auxiliary slack variables and parameter‐dependent Lyapunov functions are employed in addition to well‐established performance conditions. Then, sufficient conditions for the desired gain‐scheduled mixed‐objective robust dynamic output feedback controllers are cast into an efficiently tractable finite‐dimensional convex optimization problem in terms of linear matrix inequalities (LMIs). Finally, numerical simulation shows the validity of the proposed controller, which has good stability, strong robustness, satisfied disturbance attenuation ability, and smooth dynamic properties.

This paper presents the design and implementation of optimal and robust state feedback controller for rotary inverted pendulum system. The Particle Swarm Optimization (PSO) method is used to find the optimal values of the state feedback gains subject to time response specifications and H_∞ constraints. To improve the tracking of the system, a robust state feedback plus integral controller is designed. The simulation results show that the proposed controller can effectively stabilize the pendulum at the upright position. Further, the proposed controller can compensate the variations in system parameters. The effectiveness of the proposed controller is verified experimentally using real rotary inverted pendulum.