Real-Time Nonlinear Programming by Amplitude Modulation

The nonlinear programming (NLP) is an optimization technique that minimizes arbitrary nonlinear cost functions. To apply the NLP to real-time applications, however, the estimation of the gradient of the cost function is remained as a challenge. The extremum-seeking control (ESC) optimizes the cost functions in real-time, but it involves the complicated design of filters for simultaneous estimation of the gradient. In this paper, a complementary method that optimizes an arbitrary multivariable cost function in real-time is proposed. Taking the advantages of both NLP and ESC, the variables are updated by the steepest descent method of NLP, while the gradient of the cost function is continuously estimated by the amplitude modulation as in ESC. Unlike the ESC, the proposed method does not require the design of complicated filters. The optimization performance is verified by simulations on time-varying and noisy cost functions, as well as automatic controller tuning applications.