An algorithm for approximate calculation of the attainable sets of the nonlinear control systems with integral constraint on controls

In this paper, an algorithm for approximate calculation of the attainable sets of nonlinear control systems with integral constraint on controls is presented. A numerical example of the computer application of this algorithm is also given.     

On the supervisory control of multi-agent product systems: Controllability properties

Multi-Agent (MA) product systems were defined in [I. Romanovski, P.E. Caines, On the supervisory control of multi-agent products systems, IEEE Trans. Automated Control 51(5) (2006)] where the notion of an MA controllable vector language specification was introduced and necessary and sufficient conditions for the existence of a supervisor for such a specification were derived. In this paper we present a set of results about the controllability of an MA product system and its components. In particular, we obtain an algorithm for finding the infimal MA-controllable superlanguage inf_MA(K) of a given vector (language) specification K w.r.t. an MA product system G and establish that in fact . It is proven that there is an algorithmic procedure for the recursive construction of MA supervisors when additional automata are added to a system via the MA product. Controllability properties of component structures (such as standard controllability and MA controllability of projections) are considered. Several examples are given to illustrate the results of the paper.     

Admissible controls and attainable states for a class of nonlinear systems with general constraints

We consider nonlinear control systems where the control and the state variables are submitted to explicit constraints. This paper has two objectives. First, for a class of nonlinear systems with constraints, an existence result of nontrivial admissible controls and some of their interesting properties are proved. Then, we investigate the problem of local controllability in a neighbourhood of an equilibrium point, while observing state and control constraints along the whole trajectory. An iterative procedure is also given, which allows one to compute the steering admissible control function. This procedure is illustrated with a classical example.     

Controllability for a class of simple Wiener–Hammerstein systems

Controllability for a class of simple Wiener–Hammerstein systems is considered. Necessary and sufficient conditions for dead-beat and complete controllability for these systems are presented. The controllability tests consist of two easy-to-check tests for the subsystems.     

Controllability and reachability criteria for switched linear systems

This paper investigates the controllability and reachability of switched linear control systems. It is proven that both the controllable and reachable sets are subspaces of the total space. Complete geometric characterization for both sets is presented. The switching control design problem is also addressed.     

Controllability and stabilizability of a networked control system with periodic communication constraints

This paper proposes a new model for a networked control system and considers its controllability and stabilizability. To control a linear time-invariant discrete-time plant via a bus with limited capacity, we introduce a hold device and a communication sequence which follows a given ω-periodic pattern. Incorporating the communication sequences and hold device into the original plant amounts to extending the original time-invariant state equation to a ω-periodic one which has the higher order. We assume that the communication sequence is admissible. It is shown that controllability and stabilizability of the plant are preserved in the periodic extended system under the assumption that the zeros of the communication sequence characteristic polynomial do not coincide with the eigenvalues of the plant.     

Controllability for Discrete Systems with a Finite Control Set

In this paper we consider the problem of controllability for a discrete linear control system x _k+1=Ax _k+Bu _k, u _k∈U, where (A,B) is controllable and U is a finite set. We prove the existence of a finite set U ensuring density for the reachable set from the origin under the necessary assumptions that the pair (A,B) is controllable and A has eigenvalues with modulus greater than or equal to 1. In the case of A only invertible we obtain density on compact sets. We also provide uniformity results with respect to the matrix A and the initial condition. In the one-dimensional case the matrix A reduces to a scalar λ and for λ>1 the reachable set R(0,U) from the origin is?

Controllability and observability of switched multi-agent systems

This paper considers controllability and observability of switched multi-agent systems, which are composed of continuous-time and discrete-time subsystems. First, a controllability criterion is established in terms of the system matrices. Then, by virtue of the concepts of the invariant subspace and the controllable state set, a method is proposed to construct the switching sequence to ensure controllability of switched multi-agent systems, and a necessary and sufficient condition is obtained for controllability. Moreover, a necessary controllability condition is derived in terms of eigenvectors of the Laplican matrix. With respect to observability, two necessary and sufficient algebraic conditions are obtained. Finally, simulation examples are provided to illustrate the theoretical results.     

Controllability of linear stochastic systems

We discuss several concepts of controllability for stochastic systems and derive sufficient (and in most cases also necessary) algebraic conditions for the controllability of the state and the output of white and colored noise linear systems. These criteria reduce to the well known deterministic ones in the absence of noise.     

Controllability for single-input mechanical control systems with dissipation

Within the affane connection framework of Lagrangian control systems, based on the results of Sussmann on small-time locally controllability of single-input affine nonlinear control systems, the controllability results for mechanical control systems with single-input are extended to the case of the systems with isotropic damping, where the Lagrangian is the kinetic energy associated with a Riemannian metric, A sufficient condition of negative small-time locally controllability for the system is obtained.Then,it is demonstrated that such systems are small-time locally configuration controllable if and only if the dimemion of the configuration manifold is one. Finally, two examples are given to illustrate the results. Lie bracketting of vector fields and the symmetric product show the advantages in the discussion.     

Invertibility of affine nonlinear control systems: a geometric approach

The paper deals with the invertibility of multivariable non-linear control systems. By using the recently developed theory on controlled invariant and controllability distributions necessary and sufficient conditions for invertibility are derived.     

Controllability of nonlinear systems consisting of a bilinear mode with time-varying delays in control

Sufficient conditions are established for the global relative controllability of nonlinear system consisting of a bilinear mode with time-varying delays in control. The results are a generalization of previous results and are obtained by using Schauder's fixed point theorem.     

Controllability of probabilistic Boolean control networks

This paper deals with the controllability of probabilistic Boolean control networks. First, a survey on the semi-tensor product approach to probabilistic Boolean networks is given. Second, the controllability of probabilistic Boolean control networks via two kinds inputs is studied. Finally, examples are given to show the efficiency of the obtained results.     

Controllability of multi-agent systems with periodically switching topologies and switching leaders

This paper considers controllability of multi-agent systems with periodically switching topologies and switching leaders. The concept of m-periodic controllability is proposed, and a criterion for m-periodic controllability is established. The effect of the duration of subsystems on controllability is analysed by utilising a property of analytic functions. In addition, the influence of switching periods on controllability is investigated, and an algorithm is proposed to search for the fewest periods to ensure controllability. A necessary condition for m-periodic controllability is obtained from the perspective of eigenvectors of the subsystems’ Laplacian matrices. For a system with switching leaders, it is proved that switching-leader controllability is equivalent to multiple-leader controllability. Furthermore, both the switching order and the tenure of agents being leaders have no effect on the controllability. Some examples are provided to illustrate the theoretical results.     

Controllability and observability of Boolean control networks

The controllability and observability of Boolean control networks are investigated. After a brief review on converting a logic dynamics to a discrete-time linear dynamics with a transition matrix, some formulas are obtained for retrieving network and its logical dynamic equations from this network transition matrix. Based on the discrete-time dynamics, the controllability via two kinds of inputs is revealed by providing the corresponding reachable sets precisely. Then the problem of observability is also solved by giving necessary and sufficient conditions.     

Controllability and stability radii for companion form systems

This paper describes a unifying approach to the computation of certain robustness measures for some calculations involving state space models in control and system theory. These measures include nearness to uncontrollability, nearness to instability, and nearness to unstabilizability and their duals. Specialized results are provided for systems in companion form (controllability canonical form, etc.). It is shown analytically why high-order companion system models have certain undesirable numerical properties. For example, it is shown that almost all highorder companion matrices are nearly singular and almost all high-order controllable canonical forms are nearly uncontrollable. This research was supported by the Office of Naval Research under Contract No. N00014-85-K-0553 and the National Science Foundation (and AFOSR) under Grant No. ECS-8718897.     

Controllability and stability of repetitive batch processes

Batch control has traditionally addressed the problems related to the absence of a steady-state and the finite batch duration. Recently, batch control has added the dimension that arises naturally from the possibility of applying run-to-run control, i.e. it exploits the fact that most batch process are repeated over time. Hence, batch control calls for tools that are tailored to these new challenges and specificities of batch operations. These include a mathematical representation that explicitly shows the two independent time variables (the run time t and the run index k), two types of inputs (both constant and time-varying within a run) as well as two types of outputs (the run-time and run-end outputs). This paper introduces a definition of batch-output controllability that considers the two types of inputs and outputs. Also, a quantitative notion of stability that takes into account the finite-time nature of batch processes and typical phenomena such as the batch kick is presented. The tools required for evaluating these properties are readily adapted from the literature. As illustration, a semi-batch reactor example is considered in simulation. Various approaches to batch control are demonstrated and the associated controllability and stability issues discussed.