Avoidance Control on Time Scales

We consider dynamic systems on time scales under the control of two agents. One of the agents desires to keep the state of the system out of a given set regardless of the other agent's actions. Leitmann's avoidance conditions are proved to be valid for dynamic systems evolving on an arbitrary time scale.Comment: Revised edition in JOTA format. To appear in J. Optim. Theory Appl. 145 (2010), no. 3. In Pres

Null-Controllability of Linear Systems on Time Scales

The purpose of the paper is to study the problem of controllability of linear control systems with control constrains, defined on a time scale. The obtained results extend the existing ones on any time domain. The set of values of admissible controls is a given closed and convex cone with nonempty interior and vertex at zero or is a subset of containing zero

Linear q-Difference Fractional-Order Control Systems with Finite Memory

The formula for the solution to linear q-difference fractional-order control systems with finite memory is derived. New definitions of observability and controllability are proposed by using the concept of extended initial conditions. The rank condition for observability is established and the control law is stated

Local controllability of nonlinear discrete-time fractional order systems

The Riemann-Liouville, Caputo and Gr¨unwald-Letnikov fractional order difference operators are discussed and used to state and solve the controllability problem of a nonlinear fractional order discrete-time system. It is shown that independently of the type of fractional order difference, such a system is locally controllable in q steps if its linear approximation is globally controllable in q steps

Realizations of linear control systems on time scales

Linear constant-coefficients control systems with output on arbitrary time scales are studied. Kalman criteria of controllability and observability are extended to such systems. The main problem is to find criteria for an abstract input/output map to have a realization as a system on the time scale. Two different characterizations of realizability are proved. They extend the classical results obtained for continuous-time and discrete-time systems. Minimal realizations and their uniqueness are also studied

Avoidance control on time scales

We consider dynamic systems on time scales under the control of two agents. One of the agents desires to keep the state of the system out of a given set regardless of the other agent's actions. Leitmann's avoidance conditions are proved to be valid for dynamic systems evolving on an arbitrary time scale. © Springer Science+Business Media, LLC 2010

The Riemann-Stieltjes integral on time scales

We study the process of integration on time scales in the sense of Riemann-Stieltjes. Analogues of the classical properties are proved for a generic time scale, and examples are given. © 2010 Austral Internet Publishing. All rights reserved

Reducibility condition for nonlinear discrete-time systems: behavioral approach

The paper addresses the problem of reducibility of nonlinear discrete-time systems, described by implicit higher order difference equations where no a priori distinction is made between input and output variables. The reducibility definition is based on the concept of autonomous element. We prove necessary reducibility condition, presented in terms of the left submodule, generated by the row matrix, describing the behavior of the linearized system, over the ring of left difference polynomials. Then the reducibility of the system implies the closedness of the submodule, like in the linear time-invariant case. In the special case, when the variables may be specified as inputs and outputs and the system equations are Niven in the explicit form, the results of this paper yield the known results