Suboptimal design of intentionally nonlinear controllers

A method of designing nonlinear controls for stationary plants is presented in the paper. The objective of the design is to produce soft-saturation-type constraints on certain state variables, such as velocity or acceleration. This is accomplished by formulating the problem as an optimization of a nonquadratic performance index. A sequence of suboptimal controls is then obtained. Although this sequence converges to the exact optimum solution, the procedure is stopped when the complexity of the resulting non-linear controller exceeds the design considerations of cost, size, and/or reliability. Experimental results of an actual design clearly indicate the desired velocity saturation effects.     

Optimal linear control systems with incomplete state measurements

Optimal control laws usually require the complete measurement of the plant state. However, in practice one often has available only a small number of measurements. A procedure is developed that leads to a dynamic feedback control law which is a function of any given set of measurements. The resulting closed-loop system is optimal for all initial states of the system in the sense of minimizing a quadratic performance index. The order of the controller depends upon the observability properties of the plant. The development is extended to time-variable problems.     

Stability of digital control with computer interruptions

This note analyzes centralized digital control systems in which feedback loops are closed through a digital computer which generates the control law. Intermittent computer interruptions result in the deterioration of control quality and may even render the system unstable. A criterion that guarantees asymptotic stability under any admissible interruption pattern is presented in this note.     

On the noninferiority of Nash equilibrium solutions

In this paperk-player nonzero sum differential games are considered. A necessary condition for the closed-loop Nash equilibrium solution to be noninferior is presented. This condition involves the rank of a matrix made up of the first partial derivatives of thekHamiltonians. This condition is also a sufficient condition for the existence of a solution with the property that if the players use this solution each player does at least as well as when the Nash solutions are used and at least one player does better.     

Minimum energy control of systems with time delay

The problem of minimizing the cost functional corresponding to minimum control energyI = intmin{0}max{infty}u^{2} dtfor the linear system with delaydot{x}(t) = Ax(t) + Bx(t - h) + cu(t)is considered. From sufficient conditions for optimality, one obtains a set of algebraic equations. Numerical solution of these equations yields the optimal control law.     

Decoupling of a class of nonlinear systems

This paper develops a sufficient condition for the decoupling of a special class of nonlinear time-invariant systems. A definition of decoupling for nonlinear systems is also provided.     

On the solution of the optimal linear control problems under conflict of interest

In the control of multi-input plants, the optimal choice of the feedback control inputs depends upon the choice of disturbance inputs by the competitor, enemy, or nature. Under that viewpoint, the formulation of the control problem under conflict of interest is translated to a differential game. This study considers a two-person conflicting situation, described by linear plant dynamics, while the performance indices are quadratic functionals. A theorem and an iterative numerical technique, based on Newton's method, are developed, for the actual computation of the closed-loop solution in the stationary case of the nonzero and zero-sum differential game. Explicit solutions are also presented for the finite terminal time problem arising in the zero-sum linear differential game, and a simple sufficient condition for the existence of such solutions is included. Two examples are solved to illustrate the procedures described.