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1. Dynamic Gain Adaptation in Linear Quadratic Regulators

   https://doi.org/10.1109/TAC.2023.3344551  

   Komaee, Arash (August 2024, IEEE Transactions on Automatic Control)

   In feedback control of dynamical systems, the choice of a higher loop gain is typically desirable to achieve a faster closed-loop dynamics, smaller tracking error, and more effective disturbance suppression. Yet, an increased loop gain requires a higher control effort, which can extend beyond the actuation capacity of the feedback system and intermittently cause actuator saturation. To benefit from the advantages of a high feedback gain and simultaneously avoid actuator saturation, this paper advocates a dynamic gain adaptation technique in which the loop gain is lowered whenever necessary to prevent actuator saturation, and is raised again whenever possible. This concept is optimized for linear systems based on an optimal control formulation inspired by the notion of linear quadratic regulator (LQR). The quadratic cost functional adopted in LQR is modified into a certain quasi-quadratic form in which the control cost is dynamically emphasized or deemphasized as a function of the system state. The optimal control law resulted from this quasi-quadratic cost functional is essentially nonlinear, but its structure resembles an LQR with an adaptable gain adjusted by the state of system, aimed to prevent actuator saturation. Moreover, under mild assumptions analogous to those of LQR, this optimal control law is stabilizing. As an illustrative example, application of this optimal control law in feedback design for dc servomotors is examined, and its performance is verified by numerical simulations. 

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2. A Multirate Adaptive Control for MIMO Systems with Application to Cyber-Physical Security

   https://doi.org/10.1109/CDC.2018.8619570  

   Jafarnejadsani, Hamidreza; Lee, Hanmin; Hovakimyan, Naira; Voulgaris, Petros (December 2018, 2018 IEEE Conference on Decision and Control)

   This paper proposes a multirate output-feedback controller for multi-input multi-output (MIMO) systems, possibly with non-minimum-phase zeros, using the L1 adaptive control structure. The analysis of stability and robustness of the sampled-data controller reveals that under certain conditions the performance of a continuous-time reference system is uniformly recovered as the sampling time goes to zero. The controller is designed for detection and mitigation of actuator attacks. By considering a multirate formulation, stealthy zero-dynamics attacks become detectable. The experimental results from the flight test of a small quadrotor are provided. The tests show that the multirate L1 controller can effectively detect the zero-dynamics actuator attack and recover stability of the quadrotor. 

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3. Dynamic intermittent Q ‐learning–based model‐free suboptimal co‐design of ‐stabilization

   https://doi.org/10.1002/rnc.4515  

   Yang, Yongliang; Vamvoudakis, Kyriakos G.; Ferraz, Henrique; Modares, Hamidreza (March 2019, International Journal of Robust and Nonlinear Control)

   Summary This paper proposes an intermittent model‐free learning algorithm for linear time‐invariant systems, where the control policy and transmission decisions are co‐designed simultaneously while also being subjected to worst‐case disturbances. The control policy is designed by introducing an internal dynamical system to further reduce the transmission rate and provide bandwidth flexibility in cyber‐physical systems. Moreover, aQ‐learning algorithm with two actors and a single critic structure is developed to learn the optimal parameters of aQ‐function. It is shown by using an impulsive system approach that the closed‐loop system has an asymptotically stable equilibrium and that no Zeno behavior occurs. Furthermore, a qualitative performance analysis of the model‐free dynamic intermittent framework is given and shows the degree of suboptimality concerning the optimal continuous updated controller. Finally, a numerical simulation of an unknown system is carried out to highlight the efficacy of the proposed framework. 

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4. Anti‐windup compensation for model reference adaptive control schemes

   https://doi.org/10.1002/rnc.7511  

   Sofrony, Jorge; Turner, Matthew C; Richards, Christopher M (June 2024, International Journal of Robust and Nonlinear Control)

   Actuator constraints, particularly saturation limits, are an intrinsic and long‐standing problem in the implementation of most control systems. Model reference adaptive control (MRAC) is no exception and it may suffer considerably when actuator saturation is encountered. With this in mind, this paper proposes an anti‐windup strategy for model reference adaptive control schemes subject to actuator saturation. A prominent feature of the proposed compensator is that it has the same architecture as well‐known nonadaptive schemes, namely model recovery anti‐windup, which rely on the assumption that the system model is known accurately. Since, in the adaptive case, the model is largely unknown, the proposed approach uses an “estimate” of the system matrices for the anti‐windup formulation and modifies the adaptation laws that update the controller gains; if the (unknown) ideal control gains are reached, the model recovery anti‐windup formulation is recovered. The main results provide conditions under which, if theidealcontrol signal eventually lies within the control constraints, then the system states will converge to those of the reference model, that is, the tracking error will converge to zero asymptotically. The article deals with open‐loop stable linear systems and highlights the main challenges involved in the design of anti‐windup compensators for model‐reference adaptive control systems, demonstrating its success via a flight control application. 

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5. Tracking Control of UAVs with Uncertainty and Input Constraints

   Ahmed, Shihab; Dong, Wenjie (June 2022, Proceedings of the American Control Conference)

   This paper considers the position and attitude tracking control problem of a vertical take-off and landing unmanned aerial vehicle with uncertainty and input constraints. Considering the parametric and non-parametric uncertainties in the dynamics of systems, a robust adaptive tracking controller is proposed with the aid of the special structure of the dynamics of the system. Considering the uncertainty and input constraints, a robust adaptive saturation controller is proposed with the aid of an auxiliary compensated system. Simulation results show the effectiveness of the proposed algorithms. 

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