Approximate MSEV State-Space Based Optimal Control of Nonlinear and Nonstationary Dynamic Systems

A new class of modified minimum state error variance (MSEV) state-space based optimal linear quadratic Gaussian (LQG) regulators for closed-loop structures with estimated feedback has been proposed in this article. The negative feedback path is designed as the cascade of the digital LQG regulator and discrete Kalman state observer. The proposed design enables tracking of a time-varying reference input using the predictive control approach. Moreover, the proposed tracking method utilizes a multivariable continuous-time Cauchy state-space model of nonlinear, nonstationary dynamic systems. The resulting control strategy is approximately optimal, as the optimality of the LQG design holds locally for each linearized model around the respective operating point and does not extend to the global nonlinear system. In this sense, starting from the prespecified nominal state trajectory to be tracked, a numerical optimization procedure minimizing the squared tracking error at each step by using the Nelder–Mead direct search simplex algorithm under the required constraints on the input signal has been developed. The LQG regulator and Kalman state observer are designed by utilizing the linear discrete-time state variable models that properly approximate the nonlinear system dynamics across the nominal state trajectory. The performance of the proposed design is validated by simulating a six-degree-of-freedom nonlinear aircraft model across typical flight regimes.