Multi-valued Control Research Articles

A general existence theorem for a multi-valued control problem

A general existence theorem for a multi-valued control problem

一类多值控制网络最优决策的半张量积求解法研究

一类多值控制网络最优决策的半张量积求解法研究

Robust Output Regulation of Strongly Passive Linear Systems With Multivalued Maximally Monotone Controls

The use of multivalued controls derived from a special maximal monotone operator are studied in this note. Starting with a strictly passive linear system (with possible parametric uncertainty and external disturbances) a multivalued control law is derived, ensuring regulation of the output to a desired value. The methodology used falls in a passivity-based control context, where we study how the multivalued control affects the dissipation equation of the closed-loop system, from which we derive its robustness properties. Finally, some numerical examples together with implementation issues are presented to support the main result.

Embedded Multivalued Control for Ceramic Manufacturing

This paper presents the realization of a prototypal embedded system which implements a new control law characterized by a fixed and quantized control set. This effort is motivated by the observation that many industrial plants with high parametric uncertainties, both for constructive simplicity and/or in order to minimize the operation cost, are usually commanded with signals that can only assume a finite number of values. This paper proposes a new multivalued control algorithm which is robust with respect to disturbances and plant's uncertain parameters and consents the plant's output to practically track a given reference trajectory, with preassigned maximum values of the tracking error and its first derivative. Moreover, this paper deals with the digital realization of this new multivalued control law and the key issues associated with its microprocessor implementation. The efficiencies of the methodology and of the design procedure utilized for the realization of the embedded system are shown through a very interesting application: a temperature control system for a ceramic kiln.

ALGEBRAIC APPROACH TO DYNAMICS OF MULTIVALUED NETWORKS

Using semi-tensor product of matrices, a matrix expression for multivalued logic is proposed, where a logical variable is expressed as a vector, and a logical function is expressed as a multilinear mapping. Under this framework, the dynamics of a multivalued logical network is converted into a standard discrete-time linear system. Analyzing the network transition matrix, easily computable formulas are obtained to show (a) the number of equilibriums; (b) the numbers of cycles of different lengths; (c) transient period, the minimum time for all points to enter the set of attractors, respectively. A method to reconstruct the logical network from its network transition matrix is also presented. This approach can also be used to convert the dynamics of a multivalued control network into a discrete-time bilinear system. Then, the structure and the controllability of multivalued logical control networks are revealed.

Properties of the set of admissible “state-control” pairs for first-order evolution control systems

We consider a control system described by a non-linear first-order evolution equation on an evolution triple of Banach spaces (a “Gelfand triple”) with a mixed multivalued control constraint whose values are non-convex closed sets in the control space. Besides the original system, we consider systems with the following control constraints: the constraint whose values are the closed convex hulls of the values of the original constraint, and the constraint whose values are the extreme points of the convexified constraint that belong to the original one. We study topological properties of the sets of admissible “state-control” pairs for the same system with various constraints and consider the relations between them. An example of a non-linear parabolic control system is worked out in detail.

Minimax control of maximal monotone differential inclusions in ℝN

Minimax optimal control problems driven by a maximal monotone operator and a multivalued control vector field are examined. First the existence of optimal controls is established. Then their variations are examined as well as the variations of the value of the problem as its data are perturbed (sensitivity analysis). Finally a necessary and sufficient condition for minimax optimality is obtained.