Linear Tracking Problem Research Articles

Attracting Cylinder Method: Solution of the General Linear Tracking Problem

Attracting Cylinder Method: Solution of the General Linear Tracking Problem

Optimal Controller for Near-Space Interceptor with Actuator Saturation

The saturation of the actuator impairs the response performance of the near space interceptor control system. A control system based on the properties of linear tracking system is designed for this problem. The properties are that the maximum value of the pseudo-Lyapunov function of the linear tracking control system do not present at the initial state but at the steady state, based on which the bounded stability problem is converted into linear tracking problem. The pseudo-Lyapunov function of the linear tracking system contain the input variables; the amplitude and frequency of the input variables affect the stability of the nonlinear control system. Designate expected closed-loop poles area for different input commands and obtain a controller which is function of input variables. The coupling between variables and linear matrices make the control system design problem non-convex. The non-convex problem is converted into a convex LMI according to the Shur complement lemma and iterative algorithm. Finally the simulation shows that the designed optimal control system is quick and accurate; the rationality of the presented design techniques is validated.

Tracking control of linear switched systems

AbstractThis paper deals with the optimal tracking problem for switched systems, where the control input, the switching times and the switching index are all design variables. We propose a three-stage method for solving this problem. First, we fix the switching times and switching index sequence, which leads to a linear tracking problem, except different subsystems are defined in their respective time intervals. The optimal control and the corresponding cost function obtained depend on the switching signal. This gives rise to an optimal parameter selection problem for which the switching instants and the switching index are to be chosen optimally. In the second stage, the switching index is fixed. A reverse time transformation followed by a time scaling transform are introduced to convert this subproblem into an equivalent standard optimal parameter selection problem. The gradient formula of the cost function is derived. Then the discrete filled function is used in the third stage to search for the optimal switching index. On this basis, a computational method, which combines a gradient-based method, a local search algorithm and a filled function method, is developed for solving this problem. A numerical exampleis solved, showing the effectiveness of the proposed approach.

RECURSIVE STATE ESTIMATION FOR DISTRIBUTED PARAMETER UNCERTAIN SYSTEMS WITH INTEGRAL QUADRATIC CONSTRAINTS

The problem of recursive state estimation for a class of distributed parameter systems with an integral quadratic constraint in Hilbert spaces is addressed. Based on solving the linear tracking problem for time-varying systems in Hilbert spaces, necessary and sufficient conditions for robust state estimation problem involving construction of the set of all possible states at the finite interval time with given output measurements and integral quadratic constraints are derived.

Guaranteed cost control of tracking problems with large plant uncertainty

ABSTRACT A linear tracking problem with large plant uncertainty is studied. The guaranteed cost method is applied to design the controller so that the system responses follow the reference model. A modified Riccati matrix equation is obtained. From the numerical simulation of a second-order system, it is shown that the present method provides good performance in both tracking property and sensitivity immunity.

A continuous-time linear tracking problem with an asymmetric quadratic objective functional containing a cost-free interval.

We solve an optimal control problem with an asymmetric quadratic objective functional containing a ‘cost-free’ interval. If the state variable falls within the specified ‘cost-free’ interval, the system incurs no cost at all. The cost of overshooting or undershooting this interval is asymmetric quadratic. The problem is transformed into an equivalent control problem with state and control variable inequality constraints. We develop the reciprocal (dual) of the latter, which turns out to be a linear regulator problem with simple control-variable non-negativity constraints. Using the solution to the regulator problem, one can easily generate the solution to the original problem.

Deconvolution and linear tracking problem

The deconvolution problem is considered in this paper as an application of the optimal control theory. After the presentation of the inverse convolution in the free noise case, its application in the presence of noise is developed using the concepts of optimal filtering.

An Inverse Optimal Control Problem and Its Application to the Choice of Performance Index for Economic Stabilization Policy

The specification of a performance criterion is one of the basic requirements for the formal analysis of quantitative decision processes. A procedure of quantitatively selecting the performance index for economic stabilization policy by solving the so-called inverse optimal control problem is developed. When a closed-loop system with a known control policy is given, the inverse optimal control problem is to determine performance indices for which the given control rule is optimal. A sufficient condition is developed for the solution of the inverse problem for long-run economic stabilization policy, and an explicit solution is obtained for short-run economic stabilization policy by considering a special case where the performance index does not penalize the costs of implementing control policies. The solution of the inverse problem is found to be not unique in general, which implies that the optimal control policies are fairly robust against different performance indices. Also, it is found that the solution of the inverse problem for a linear regulator holds true for the linear tracking problem, which makes the analysis much simpler. A procedure is developed for the selection of the performance index along with the optimal feedback control policy by which the economic system is to reveal the desired characteristics. The procedure demonstrates the determination of the steady states as policy goals, the computation of the feedback control policy, and the construction of a performance index, through a small econometric model.

Optimal and suboptimal performance of stochastic linear tracking systems

The derivation of performance indices for both optimal and suboptimal linear tracking systems is organised so that the expressions for the indices consist of terms that may be calculated from the system input and its parameters and which represent separately various identifiable components of the overall cost. The derivation of the performance index for optimal linear tracking systems is necessary to give a complete solution to the optimal linear tracking problem. A knowledge of the various cost terms in the performance index of suboptimal linear tracking systems means that the performance of existing or approximate designs, or of optimal designs either modified or having different noise inputs or performance indices, may be calculated. Further, the improvement of existing or approximate designs may be carried out by a systematic trial-and-error approach, which aims at reducing perhaps only the largest cost terms for each iteration.