Abstract
This paper considers the optimal control problem for the bilinear system based on state feedback. Based on the concept of relative order of the output with respect to the input, first we change a bilinear system to a pseudo linear system model through the coordinate transformation. Then based on the theory of linear quadratic optimal control, the optimal controller is designed by solving the Riccati equation and introducing state feedback with state prediction. At last, the simulation results in CSTR Chemical reactor show the effectiveness of the method.
Highlights
Bilinear system is a special nonlinear system, during the processes of the engineering, social economy and ecology, there are so many objects can be described by bilinear systems
This paper considers the optimal control problem for the bilinear system based on state feedback
Aganovic proposed a method of global successive approximation about bilinear system [1,2]; DISOPE approximate algorithm based on bilinear model is presented by Li [3]; Tang has studied the optimal control of the discrete bilinear system [4,5,6]
Summary
Bilinear system is a special nonlinear system, during the processes of the engineering, social economy and ecology, there are so many objects can be described by bilinear systems. The optimal iterative algorithm based on quadratic performance index about bilinear system is given in the reference [8], etc. This paper concentrates on the solution of the optimal control problem for bilinear systems with a quadratic criterion based on state feedback. The nonlinear system model; Secondly, a complex nonlinear system model is changed to an easy pseudo linear system model by the differential homeomorphism; the optimal control law is designed by solving the Riccati equation; performance of the obtained optimalcontrol for bilinear systems with a quadratic criterion is verified in the CSTR Chemical reactor example. Simulation graphs demonstrating better performance of the obtained optimal regulator are included
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