Optimal control of discrete-time linear fractional-order systems with multiplicative noise

ABSTRACT

A finite horizon linear quadratic (LQ) optimal control problem is studied for a class of discrete-time linear fractional systems (LFSs) affected by multiplicative, independent random perturbations. Based on the dynamic programming technique, two methods are proposed for solving this problem. The first one seems to be new and uses a linear, expanded-state model of the LFS. The LQ optimal control problem reduces to a similar one for stochastic linear systems and the solution is obtained by solving Riccati equations. The second method appeals to the principle of optimality and provides an algorithm for the computation of the optimal control and cost by using directly the fractional system. As expected, in both cases, the optimal control is a linear function in the state and can be computed by a computer program. A numerical example and comparative simulations of the optimal trajectory prove the effectiveness of the two methods. Some other simulations are obtained for different values of the fractional order.

KEYWORDS:

• Fractional discrete-time systems
• linear quadratic control
• multiplicative noise
• dynamic programming

MSC 2010:

• 93CXX
• 93C55

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

FEDER and Ministerio de Economía y Competitividad, Government of Spain [grant number MTM2013-41704-P].