A discrete-time adaptive control law for stabilization, command following, and disturbance rejection that is effective for systems that are unstable, MIMO, and/or nonminimum phase. The adaptive control algorithm includes guidelines concerning the modeling information needed for implementation. This information includes the relative degree, the first nonzero Markov parameter, and the nonminimum-phase zeros. Except when the plant has nonminimum-phase zeros whose absolute value is less than the plant's spectral radius, the required zero information can be approximated by a sufficient number of Markov parameters. No additional information about the poles or zeros need be known. Numerical examples are presented to illustrate the algorithm's effectiveness in handling systems with errors in the required modeling data, unknown latency, sensor noise, and saturation.

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The aerodynamics of micro air vehicles (operating at the chord Reynolds number of 10 5 or below) is substantially influenced by the unsteadiness of the wind gust and the aircraft's light weight. In this effort, we investigate the active flow control of the dielectric barrier discharge actuator for flows around the SD7003 airfoil, with the chord Reynolds number of 6×10 4 , to enhance our understanding of the unsteady aerodynamics. Using a recently developed ARMARKOV/Toeplitz control scheme, the characteristics of the adaptive control in response to the fluctuation of the free stream, and impact on the aerodynamics are probed. By varying the voltage amplitude to the DBD actuator, effective control of unsteady flow structure can be performed to attain a desirable lift.

We construct multivariable internal model controllers in the shift and delta domains. To do so, we develop a linear algebraic approach to the multivariable command following and disturbance rejection problem that facilitates a unified treatment of the differential, shift, and delta domains.

In this paper we use a retrospective correction filter (RCF) to identify MIMO LTI systems. This method uses an adaptive controller in feedback with an initial model. The goal is to adapt the closed-loop response of the system to match the response of an unknown plant to a known input. We demonstrate this method on numerical examples of increasing complexity where the initial model is taken to be a onestep delay. Minimum-phase and nonminimum-phase SISO and MIMO examples are considered. The identification signals used include zero-mean Gaussian white noise as well as sums of sinusoids. Finally, we examine the robustness of this method by identifying these systems in the presence of actuator noise.

The backup control barrier function (CBF) was recently proposed as a tractable formulation that guarantees the feasibility of the CBF quadratic programming (QP) via an implicitly defined control invariant set. The control invariant set is based on a fixed backup policy and evaluated online by forward integrating the dynamics under the backup policy. This paper is intended as a tutorial of the backup CBF approach and a comparative study to some benchmarks. First, the backup CBF approach is presented step by step with the underlying math explained in detail. Second, we prove that the backup CBF always has a relative degree 1 under mild assumptions. Third, the backup CBF approach is compared with benchmarks such as Hamilton Jacobi PDE and Sum-of-Squares on the computation of control invariant sets, which shows that one can obtain a control invariant set close to the maximum control invariant set under a good backup policy for many practical problems.

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