Experimental Results of Optimal and Robust Control for Uncertain Linear Time-Delay Systems

Comments on the Bellman functional for linear time‐delay systems

“…Clearly, this table gives experimental evidence to conclude that the optimal control for time delay systems has a better performance than the optimal PI control. In contrast with previous results, 16 it is possible to use a linear model only for the prototype, if it is improved with an adaptive scheme.…”

“…where h is the delay induced by the hot air recycling loop, the state variable x(t) is the temperature value, the control input u(t) is the energy applied to the actuator and the initial condition is =17 • C. It is reported in the literature that the poor performance observed 16 when using a linear model of the form (32) can be improved 17,18 by using a nonlinear model with nominal linear part given by (32). Here, we introduce an adaptive scheme based on the online Recursive Least Square method: 19 the estimated model parameters converge to a 0 = −0.079931, a 1 = 0.053467, and b = 0.002374.…”

“…20 We chose Q = 15 and R = 1 in the performance index (2), and for the identified parameters, we solve the set of Equation (27) numerically as in Ross. 3 The digital implementation of the optimal control is explained in López-Labra et al 16 Figure 2 displays the time behavior of the plant parameters and their convergence.…”