Optimal control of linear time-varying systems using the Chebyshev wavelets (a comparative approach)

Abstract

This paper extends the application of continuous Chebyshev wavelet expansions to find the optimal solution of linear time-varying systems using two different approaches. By using the product of two time functions together with the operational matrix of integration, the system of state equations are changed into a set of algebraic equations which can be solved using a digital computer. In addition, the Chebyshev wavelets are more successful to find the optimal solution of linear time-varying systems when compared with the other existing mentioned algorithms. Finally, the main feature of this paper over similar possible works is that the use of the Lagrange multipliers approach gives more accurate results in comparison with the results of the Riccati approach. The given examples support these claims.