Optimal control for linear systems described by $m$-times integrated semigroups

In this article, we prove the continuity property of the Combined $L^{1}-L^{2}$ (CLOT) optimal control for linear systems. For this, we give first-order necessary conditions for the CLOT optimal control problem based on the non-smooth maximum principle. From these necessary conditions, we prove that if the problem is normal, then the CLOT optimal control (if it exists) is continuous with respect to time. Simulation results are shown to illustrates the continuity property of the CLOT optimal control.

The optimal control of linear systems where measurement of all the state variables is not possible is investigated from the viewpoint of observer theory. Observers whose dynamic order equals the dimension of the plant state vector are examined and necessary conditions for the optimal observer dynamics and control feedback gains are derived.

We consider a finite-horizon linear-quadratic optimal control problem where only a limited number of control messages are allowed for sending from the controller to the actuator. To restrict the number of control actions computed and transmitted by the controller, we employ a threshold-based event-triggering mechanism that decides whether or not a control message needs to be calculated and delivered. Due to the nature of threshold-based event-triggering algorithms, finding the optimal control sequence requires minimizing a quadratic cost function over a nonconvex domain. In this paper, we first provide an exact solution to this nonconvex problem by solving an exponential number of quadratic programs. To reduce computational complexity, we then propose two efficient heuristic algorithms based on greedy search and the alternating direction method of multipliers technique. Later, we consider a receding horizon control strategy for linear systems controlled by event-triggered controllers, and we further provide a complete stability analysis of receding horizon control that uses finite-horizon optimization in the proposed class. Numerical examples testify to the viability of the presented design technique.

Optimal linear regulator problems solved by the finite element method

This correspondence considers the problem of optimal regulator design for discrete time linear systems subjected to white state-dependent and control-dependent noise in addition to additive white noise in the input and the observations. A pseudo-deterministic problem is first defined in which multiplicative and additive input disturbances are present, but noise-free measurements of the complete state vector are available. This problem is solved via discrete dynamic programing. Next is formulated the problem in which the number of measurements is less than that of the state variables and the measurements are contaminated with state-dependent noise. The inseparability of control and estimation is brought into focus, and an enforced separation solution is obtained via heuristic reasoning in which the control gains are shown to be the same as those in the pseudo-deterministic problem. An optimal linear state estimator is given in order to implement the controller.

Time optimal control for linear systems on Lie groups

The satisfactory optimal control of linear systems under the existence of disturbance is studied. The satisfactory optimal control optimizes a quadratic maximal-valued objective functional subject to the H/sub /spl infin// norm constraint. We obtain Riccati-type equations by which the satisfactory optimal control is calculated in a form of state feedback.

Fuzzy Optimal Control of Linear Systems. Part 1. Positional Control

The stochastic optimal control of linear systems with time-varying and partially observable parameters is synthesized under noisy measurements and a quadratic performance criterion. The structure of the regulator is given, and the optimal solution is reduced to a two-point boundary-value problem. Comments on the numerical solution by appropriate integration schemes is included.

Optimal feedback stabilization policy with asymmetric loss functions

A linear time-varying optimal control system with a quadratic performance index is solved by using piecewise-linear polynomial functions. Only a small number of basis functions are needed to produce a satisfactory result, and the outcome is much better than the solutions obtained by using Walsh functions, block-pulse functions or Taylor polynomial series. Owing to the available recursive formula, the computational work is convenient and straightforward.

Neural network learning of optimal Kalman prediction and control

The paper introduces a new method for finding optimal control of algebraic dynamic systems. The structure of algebraic dynamical systems is nonlinear with quadratic and bilinear terms. A new hybrid extended Fourier series is introduced, and state and control variables of the system are expanded by this series. Moreover, properties of new series are presented, and integration and product operational matrices are obtained. Using operational matrices, optimal control of the systems is converted to a set of simultaneous nonlinear algebraic relations. An illustrative example is included to compare our results with those in the literature.

The problem of optimal control of time-varying linear singular systems with quadratic performance index has been studied using the Runge–Kutta–Butcher algorithm. The results obtained using the Runge–Kutta (RK) method based on the arithmetic mean (RKAM) and the RK–Butcher algorithms are compared with the exact solutions of the time-varying optimal control of linear singular systems. It is observed that the result obtained using the RK–Butcher algorithm is closer to the true solution of the problem. Stability regions for the RKAM algorithm, the single-term Walsh series method and the RK–Butcher algorithms are presented. Error graphs for the simulated results and exact solutions are presented in graphical form to highlight the efficiency of the RK–Butcher algorithm. This algorithm can easily be implemented using a digital computer. An additional advantage of this method is that the solution can be obtained for any length of time for this type of optimal control of time-varying linear singular systems.

The optimal control system represented by a linear integral equation with a quadratic cost function is considered. Necessary conditions for optimality are derived and an iterative method of solution is presented.