Time-optimal control under state-dependent control restraints

We consider the control system $$\dot x = Ax + Bu,$$ subject to the state-dependent control restraint $$u(t) \in \Omega \cap (\mathcal{H}{\text{ + }}Cx(t)\} ,$$ where Ω is a compact convex set, ? is a subspace, andC is a matrix. The existence of time-optimal maximal controls is proven. A natural application of this result is in solving time-optimal problems under the control restraintu(t)∈Ω and the requirement that the outputy=Sx be maintained at zero during the transfer, whereS is a given matrix. An example is provided.     

Fuzzy control with limited control opportunities and response delay––a production-inventory control scenario

This paper examines the utility of fuzzy control over crisp in situations where the control opportunities are limited and the system response to control actions is delayed. Such situations are often encountered in production systems where limited resources restrict the control opportunities and the operation time delays the response. The performance of a real-time production-inventory control system is studied with fuzzy control strategy and compared with a corresponding crisp control and no-control strategy. The system consists of a production shop having a number of identical processing machines which produce two products. The output goes into two bins whose inventory is required to be controlled at desired level by varying the number of machines allocated to the products. Real-time inventory variation, output, average inventory and machine usage, number of setups and stock-outs are used as performance measures. The simulation results of the system with various configurations show that the capability of fuzzy control is seriously inhibited by limited opportunities and response delay although fuzzy has distinct advantage over crisp. As control opportunities increase fuzzy control becomes increasingly efficient with diminishing effect of response delay.     

Optimal control with a cost on changing control

In this paper, we consider a class of optimal control problems in which the cost functional is the sum of the terminal cost, the integral cost, and the full variation of control. The term involving the full variation of control is to measure the changes on the control action. A computational method based on the control parametrization technique is developed for solving this class of optimal control problems. This computational method is supported by a convergence analysis. For illustration, two numerical examples are solved using the proposed method.This project was partially supported by an Australian Research Grant.This paper is dedicated to Professor L. Cesari on the occasion of his 80th birthday.     

Research on stochastic control of networked control systems

A new control mode is proposed for networked control systems whose network-induced delay is longer than a sampling period. Under the control mode, the mathematical model of networked control systems is obtained. Markov characteristic of the network-induced delay is discussed. Based on Markov chain theory, the optimal controller is designed. One example is given for illustration.     

Congestion control using dynamic routing and flow control

In this paper, the congestion control in store and forward computer com-munication networks is studied, the method employed consists of a combination of a dynamic routing policy that minimizes the delay, and buffer nianagement schemes to control the flow of data. Simulation using liner programming has been carried out, under balanced and transient traffic conditions, on a simple 3–node network , the relative merits and drawbacks of each approach are discussed. Irland [2], showed that with static routing, the SQRT scheme improves the switch performance. In this paper it is shown that in the case of dynamic routing, the SQRT is an excellent solution to remedy the performance degradation caused by CP and CS schemes     

Application of vibrational control to linear-quadratic control problems

The application of the theory of vibrational control to linear-quadratic control problems is developed. The solution of the matrix Riccati differential equation (RDE) and the optimal trajectory are found approximately as power series of a small parameter. The minimizing effect of vibrations on the maximal solution of RDE and the cost functional is studied. The region of attraction of the maximal solution of RDE for the case of Hamiltonian matrix with imaginary axis eigenvalues is found. Special attention is paid to the application of vibrations to the linear-quadratic problem of stabilization with respect to a part of variables and transfer of the other variables to a given position. A problem of vibrational stabilization and optimal control of a carriage with an inverted pendulum is solved as an example.     

Hierarchic control

Distributed control is applied to a system modelled by a parabolic evolution equation. One considers situations where there are two cost (objective) functions. One possible way is to cut the control into 2 parts, one being thought of as “the leader” and the other one as “the follower”. This situation is studied in the paper, with one of the cost functions being of the controllability type. Existence and uniqueness is proven. The optimality system is given in the paper. Dedicated to the memory of Professor K G Ramanathan     

Avoidance control

We consider dynamical systems subject to control by two agents, one of whom desires that no trajectory of the system, emanating from outside a given set, intersects the set, no matter what the admissible actions of the other agent. Conditions are given whose satisfaction assures that a given control results in avoidance. Furthermore, these conditions are constructive in that they yield an avoidance feedback control. Some examples are presented.     

On infinite-dimensional control systems with state and control constraints

In this paper we examine infinite-dimensional control systems governed by semilinear evolution equations and having both state and control constraint. We introduce the relaxed system and show that the original trajectories are dense in an appropriate function space in the relaxed ones. We also determine the dependence of the solution set on the initial conditions. Then using those results we establish necessary and sufficient conditions for optimality for some optimization problems. Finally we prove some controllability results.     

Finite-time chaos control via nonsingular terminal sliding mode control

This paper considers the nonsingular terminal sliding mode control for chaotic systems with uncertain parameters or disturbances. The switching surface is designed technically to realize fast convergence. The controller derived from such switching surface is nonsingular and it can stabilize the chaotic systems in a finite time. Besides the second-order system and the triangular system, the proposed method can also be applied to a general class of uncertain nonlinear system. Finally, simulation results are presented to illustrate the effectiveness of the design.     

Robust reliable dissipative control of nonlinear networked control systems

This article focuses on the robust reliable dissipative control issue for a class of switched discrete‐time nonlinear networked control systems with external energy bounded disturbances. In particular, nonlinearities are modeled in a probabilistic way according to Bernoulli distributed white sequence with known conditional probability. A Lyapunov–Krasovskii functional is proposed based on which sufficient conditions for the existence of the reliable dissipative controller are derived in terms of linear matrix inequalities (LMIs) which ensures exponentially stability as well as dissipative performance of the resulting closed‐loop system. The explicit expression of the desired controller gains can be obtained by solving the established LMIs. Finally, a numerical example is presented to demonstrate the effectiveness and applicability of the proposed design strategy. © 2016 Wiley Periodicals, Inc. Complexity 21: 427–437, 2016     

Multi-variable control of chaos using PSO-based minimum entropy control

The minimum entropy (ME) control is a chaos control technique which causes chaotic behavior to vanish by stabilizing unstable periodic orbits of the system without using mathematical model of the system. In this technique some controller type, normally delayed feedback controller, with an adjustable parameter such as feedback gain is used. The adjustable parameter is determined such that the entropy of the system is minimized. Proposed in this paper is the PSO-based multi-variable ME control. In this technique two or more control parameters are adjusted concurrently either in a single or in multiple control inputs. Thus it is possible to use two or more feedback terms in the delayed feedback controller and adjust their gains. Also the multi-variable ME control can be used in multi-input systems. The minimizing engine in this technique is the particle swarm optimizer. Using online PSO, the PSO-based multi-variable ME control technique is applied to stabilize the 1-cycle fixed points of the Logistic map, the Hénon map, and the chaotic Duffing system. The results exhibit good effectiveness and performance of this controller.     

Inverse optimal control and construction of control Lyapunov functions

In this paper, the construction of CLFs for nonlinear systems and a new inverse optimal control law are presented. The construction of a CLF for an affine nonlinear system is reduced to the construction of a CLF for a simpler system, and a new L _g V type control law with respect to a CLF is provided. This control law is a generalization of Sontag’s formula and contains a design parameter. Tuning this parameter gives many suboptimal solutions for the optimization problem. Also, the gain margin and sector margin of the control law are calculated. Examples are provided to illustrate the main theoretical results of the paper. Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 61, Optimal Control, 2008.     

A control reduced primal interior point method for a class of control constrained optimal control problems

A primal interior point method for control constrained optimal control problems with PDE constraints is considered. Pointwise elimination of the control leads to a homotopy in the remaining state and dual variables, which is addressed by a short step pathfollowing method. The algorithm is applied to the continuous, infinite dimensional problem, where discretization is performed only in the innermost loop when solving linear equations. The a priori elimination of the least regular control permits to obtain the required accuracy with comparatively coarse meshes. Convergence of the method and discretization errors are studied, and the method is illustrated at two numerical examples. Supported by the DFG Research Center Matheon “Mathematics for key technologies” in Berlin. This paper appeared as ZIB Report 04-38.     

Chaos synchronization and chaos control of quantum-CNN chaotic system by variable structure control and impulse control

In this paper, we derive some less stringent conditions for the exponential and asymptotic stability of impulsive control systems with impulses at fixed times. These conditions are then used to design an impulsive control law for the Quantum Cellular Neural Network chaotic system, which drives the chaotic state to zero equilibrium and synchronizes two chaotic systems. An active sliding mode control method is synchronizing two chaotic systems and controlling chaotic state to periodic motion state. And a sufficient condition is drawn for the robust stability of the error dynamics, and is applied to guiding the design of the controllers. Finally, numerical results are used to show the robustness and effectiveness of the proposed control strategy.     

Suboptimal target control for hybrid automata using model predictive control

In this paper, a computationally efficient controller is proposed for the target control problem when the system is modelled by hybrid automata. The design is carried out in two stages. First, we compute off-line the shortest switching path which has the minimum discrete cost from an initial set to the given target set. Next, a controller is derived which successfully drives the system from any given initial state in the initial set to the target set while minimizing a cost function. The model predictive control (MPC) technique is used when the current state is not within a guard set, otherwise the mixed-integer predictive control (MIPC) technique is employed. An on-line, semi-explicit control algorithm is derived by combining these two techniques. When the system is subject to additive bounded disturbance, it is shown that the proposed on-line control algorithm holds if tighter constraints on the original nominal state and controller are imposed. Finally, as an application of the proposed control procedure, the high-speed and energy-saving control problem of the CPU processing is considered.     

Sufficient conditions for optimal control with state and control constraints

A monotonicity result is utilized to derive sufficient optimality conditions of considerable generality for an individual trajectory in control theory. The sufficiency theorem embodying these conditions generalizes those of Boltyanskii and Leitmann and is applied to a simple control system to which their sufficiency theorems are not applicable. Conditions on the state equations and state space are completely relaxed. The set of admissible controls is extended to the set of measurable controls and the integrand of the performance index has its membership extended to the class of bounded Borel-measurable functions. The decomposition of the state space is required to be onlyplain denumerable.     

Output tracking control of Boolean control networks with impulsive effects

This paper studies the output tracking problem of Boolean control networks (BCNs) with impulsive effects via the algebraic state‐space representation approach. The dynamics of BCNs with impulsive effects is converted to an algebraic form. Based on the algebraic form, some necessary and sufficient conditions are presented for the feedback output tracking control of BCNs with impulsive effects. These conditions contain constant reference signal case and time‐varying reference signal case. The study of an illustrative example shows that the obtained new results are effective.     

Stability of solutions to control constrained nonlinear optimal control problems

We consider a family of nonlinear optimal control problems depending on a parameter. Under the assumption of a second-order sufficient optimality condition it is shown that the solutions of the problems as well as the associated Lagrange multipliers are Lipschitz continuous functions of the parameter.