LQ Control Problem Research Articles

The infinite time near optimal decentralized regulator problem for singularly perturbed systems: a convex optimization approach

This paper presents LQ decentralized pole location for singularly perturbed systems. The poles are located in a sector included in the left-half complex plane. The singular perturbation method is used to define reduced and well-behaved problems. It is shown that the LQ control problem with pole location in a sector can be solved using the LMI tool. The associated parametrical optimization problem involves a linear cost objective under LMI constraints. The decentralized control problem is then solved in the reduced slow system by just introducing structure constraints on the matrix variables, constraints that do not destroy the linearity and then the convexity of the problem.

A COMPUTATIONAL METHOD FOR INTERVAL MIXED VARIABLE ENERGY MATRICES IN PRECISE INTEGRATION

To solve the Riccati equation of LQ control problem, the computation of interval mixed variable energy matrices is the first step. Taylor expansion can be used to compute the matrices. According to the analogy between structural mechanics and optimal control and the mechanical implication of the matrices, a computational method using state transition matrix of differential equation was presented. Numerical examples are provided to show the effectiveness of the present approach.

Feedback stabilization of semilinear heat equations

This paper is concerned with the internal and boundary stabilization of the steady‐state solutions to quasilinear heat equations via internal linear feedback controllers provided by an LQ control problem associated with the linearized equation.

Probabilistic robust optimization of two LQ control problems

Abstract The probabilistic robust optimization (PRO) of LQ control problems arc studied in the framework of soft-bound descriptions. The improved robustness and the unity design in the parameter space are achieved by optimizing a probability-weighted sum of quadratic performances of the system with respect to possible parametric uncertainties. Two PRO problems are formulated considering real control requirements. The approach with the construction of a probability-extended system is proposed to determine the optimal control profile and the gradient-based solution is presented to find the optimal feedback control. Numerical examples illustrate the advantages of the presented methods for systems with large parametric uncertainties.

LQ preview synthesis: optimal control and worst case analysis

A generalized LQ-control problem, which treats a mixed attenuation of stored disturbance and initial state uncertainty, is discussed in the infinite-horizon time setting. The posed problem covers a part of predictive control problems and enables one to deal with the LQ optimal preview servocontroller design. For the generalized LQ problem, we first derive an optimal preview control which minimizes the LQ cost functional and provide some interpretations on the structure of resulting control law. We then analyze worst case initial uncertainties, i.e., those of initial state and the shape of stored disturbance, which maximize the cost functional of the resulting closed-loop system.

Robust LQ Control for Uncertain Linear Time-Delay Systems: A Linear Matrix Inequality Approach With Guaranteed α-Stability

In this note, we are concerned with robust LQ control problem for uncertain linear time-delay systems. More precisely, we design a memoryless static state feedback controller such that the closed-loop system is robustly α - stable for all admissible uncertainty. Furthermore, an upper bound for a given performance index is guaranteed. We show that feasibility of some LMls guarantees the solvability of this problem.

The solution for the generalized riccati algebraic equations of linear equality constraint system

Based on the dynamic equation, the performance functional and the system constraint equation of time-invariant discrete LQ control problem, the generalized Riccati equations of linear equality constraint system are obtained according to the minimum principle, then a deep discussion about the above equations is given, and finally numerical example is shown in this paper.

Constrained Regular LQ-Control Problems

In this paper we give a complete description of how the Jacobi theory of conjugate points can be extended to a regular linear-quadratic control problem where the state end-points are jointly constrained to belong to a subspace of ${\bf R}^n \times {\bf R}^n$ and there is a linear pointwise state-control constraint. We introduce also the definition of semiconjugate point which describes a distinctive feature of these problems and state the corresponding necessary and sufficient conditions for the quadratic form to be nonnegative or coercive. In the case in which the constraints and the costs act separately on the initial and final points we give equivalent characterizations of the coercivity of the quadratic form by means of the solutions of an associated Riccati equation in both the controllable and uncontrollable case.

Linearly Constrained LQ and LQG Optimal Control

It has recently been shown that the logarithmic barrier method for solving finite-dimensional, linearly constrained quadratic optimization problems can be extended to an infinite-dimensional setting with complexity estimates similar to the finite dimensional case. As a consequence, an efficient computational method for solving the linearly constrained LQ control problem is now available. In this paper, we solve the linearly constrained LQG control problem by generalizing the Separation Theorem. We show how the logarithmic barrier method can be used to determine the optimal control for the constrained LQG problem.

Linear Quadratic Optimal Feedforward/Feedback Control

A generalized type of LQ-control problem, which treats a mixed attenuation of stored disturbance and initial state uncertainty, is discussed in the infinite-horizon time setting. For the generalized LQ-problem, an optimal preview control and worst-case initial uncertainties, i.e. those of initial state and the shape of stored disturbance, which maximize the cost functional of resulting closed loop system are clarified. The posed problem covers a part of predictive control problems and enables to attack LQ optimal preview servo-controller design.

Digital control of Pritchard-Salamon systems

Abstract In this paper we are concerned with the digital approach to the LQ optimal control problem of Pritchard-Salamon systems. We show how the digital control problem can be converted into an equivalent discrete-time LQ control problem and the construction of the optimal control law is based on the solution of classical Riccati equations.

Decentralized Control of Mechatronic Systems in Descriptor Form

A decentralized controller design procedure is developed for a special class of mecha-tronic systems in descriptor form using linear quadratic methods. The decentralized system consists of mechanical subsystems with constraint equations up to index 3. Interconnections between the subsystems are limited to be of index 1. Under the assumption of regularity and causality decomposition of the global descriptor system into its Kronecker-canonical form leads to the well known decentralized LQ control problem for normal state-space systems. The advantage of having direct influence on the interconnection variables in the performance index is demonstrated in an example.

The Riccati Equation for Regular LQ-Control Problems with Constraints

In this note we consider a linear-quadratic time dependent control problem where the state end-points are constrained to affine varieties and where there is an affine pointwise state-control constraint. The problem is analyzed over a finite time interval. We characterize the existence of a unique solution by means of the existence of a solution of an associated Riccati equation. The optimal control solving the affine problem is expressed in a feed-back type form.

Optimal solution approximation for infinite positive-definite quadratic programming

We consider a general doubly-infinite, positive-definite, quadratic programming problem. We show that the sequence of unique optimal solutions to the natural finite-dimensional subproblems strongly converges to the unique optimal solution. This offers the opportunity to arbitrarily well approximate the infinite-dimensional optimal solution by numerically solving a sufficiently large finite-dimensional version of the problem. We then apply our results to a general time-varying, infinite-horizon, positive-definite, LQ control problem.

The application of the variational principle in the constrained control system

The regular equations on the constraint variables are established for LQ and nonlinear control problems in this paper, then the extreme-value principles of the constraint variables are discussed for the equality and unequality constraint cases respectively. At last, the given example verifies the conclusion of this paper. The work in this paper will lay the foundation for the further study about the constrained LQ and nonlinear control systems.

A bicriteria stationary LQ control problem

This note gives a simple derivation of the minimal loss vectors and the Pareto-optimal solutions to a certain bicriteria stationary LQ control problem.

Two-level stochastic LQ control problem for a dynamic system

Two-level, hierarchical, partially decentralized control for a large-scale system is considered. It is seen that for an LQ problem the optimal control laws are linear functions of the state estimates. The filter equations for some state estimates, determined by a coordinator and local controllers co-operating in a two-level control structure, are derived, A discussion on the usefulness of the application of particular local controllers is given, as well as a numerical example.

On the necessity of identifying the true parameter in adaptive LQ control

In adaptive control problems one may drop the requirement of identifying the true system in order to simplify the problem of control. It will be shown that in the adaptive LQ control problem this does not at all lead to an easier problem.