Control of Uncertain Dynamical Systems with Spatial and Temporal Constraints

The overarching objective of this dissertation is the development of feedback control frameworks for uncertain dynamical systems that are subject to spatial and/or temporal constraints. These spatiotemporal constraints usually arise from the physical and/or performance characteristics associated with a considered dynamical system in safety-critical applications, where synthesis and analysis of feedback control laws are not trivial. Specifically, the proposed control architectures in this dissertation mainly contribute to the model reference adaptive control and finite-time control literature. In particular, unlike existing model reference adaptive control approaches that are not capable of enforcing user-defined performance guarantees without an ad-hoc tuning process, the proposed control architectures utilize an error-dependent learning rate that enables a control designer to assign a user-defined performance bound to the system trajectories. In addition, the convergence time of the existing finite-time controllers either depends on the initial conditions of the system or the upper bound on the system uncertainties; hence, this convergence time cannot be strictly assigned by the control designer. The proposed finite-time control algorithms in this dissertation utilize a time transformation technique to address this challenge, where the resulting convergence time is independent of the initial conditions and the knowledge of upper bound of the system uncertainties. Research in adaptive control theory has demonstrated the capabilities of these feedback algorithms in suppressing the effects of adverse conditions resulting from exogenous disturbances, imperfect system modeling, degraded modes of operation, and changes in system dynamics. Yet, not only standard adaptive controllers usually yield to conservative performance bound on the system error signal, but also they require the knowledge of the upper bound on the system uncertainties to specify such a bound. Therefore, a major challenge in standard adaptive control algorithms is their inability to address control problems with a-priori given spatial constraints. In this dissertation, this critical issue is addressed by introducing the set-theoretic model reference adaptive control architecture. This approach utilizes so-called generalized restricted potential functions by incorporating a system error-dependent learning rate in the adaptation process. The resulting control architecture ensures that the system error signal evolves in a user-defined compact set for all time without the requirement of the knowledge of the upper bound on the system uncertainties. For the case where the system uncertainty is unstructured, a new neuroadaptive control architecture predicated on a set-theoretic treatment is then studied such that the closed-loop system trajectories are guaranteed to stay within the compact set without violating the universal function approximation property. As another contribution in this dissertation, the set-theoretic model reference is generalized to enforce a time-varying performance bound on the norm of system error vector. This gives a control designer the flexibility to control the closed-loop system performance as desired on different time intervals separately. In practice, a subset of system trajectories can be more critical than the others. Hence, it is desired not only to enforce a performance bound on the entire norm of the system error, but also to be able to adjust the resulting performance bound specifically for that critical subset. To address this problem, a command governor approach is embedded in the set-theoretic model reference adaptive control architecture. Actuator dynamics and actuator failures are two of the most important considerations for implementing any control algorithm. To this end, extensions of the set-theoretic model reference adaptive control architecture are proposed, where it ensures the system stability as well as the user-defined performance guarantee despite the presence of actuator dynamics or actuator failures during an operation. The applications of the proposed set-theoretic model reference adaptive control is also studied within the context of this dissertation. Specifically, this framework is implemented on a generic transport model developed by NASA on both longitudinal and lateral-directional dynamics. In addition, the proposed set-theoretic model reference adaptive control is evaluated on an aerospace testbed, which is configured as a conventional dual-rotor helicopter for enforcing constant and time-varying performance bounds. Practical implementation considerations for the set-theoretic model reference adaptive control architecture is also studied. In particular, a generalization of this control architecture with dead-zone effect is proposed where it stops the adaptation process inside the dead-zone, but it still ensures that the norm of the system error is evolving inside a user-defined performance bound. The set-theoretic model reference adaptive control is also augmented at the inner-loop control structure of human-in-the-loop control architectures to provide a sufficient stability condition for the overall physical system. Another major contribution of this dissertation is to address control problems with temporal constraints. This problem is considered in the context of networked multiagent systems, where the control objective is to drive the agents to a time-varying leader within a user-defined finite time interval. To this end, using a time transformation approach, the desired user-defined finite-time interval of interest is converted into a stretched infinite-time interval. The robustness properties of the proposed control algorithm, as well as the finite-time convergence guarantees is established in this new infinite-time interval. One can then readily transfer back the results into the original finite time interval of interest. The effects of sensor uncertainties are also studied in this dissertation, where they can significantly deteriorate the achievable closed-loop system performance in networked multiagent systems. These uncertainties may arise due to low sensor quality, sensor failure, sensor bias, or detrimental environmental conditions. To tackle this challenge, a resilient distributed control algorithm is designed to mitigate the effect of sensor uncertainties. Finally, a unified control architecture is proposed to simultaneously address the problem of spatiotemporal constraints for uncertain dynamical systems. The proposed control architecture, ensures that the agents converge to a time-varying leader at a user-defined finite time of interest, while guaranteeing user-defined performance bounds on the system error trajectories. The stability and performance properties for all of the aforementioned control architectures are rigorously established using system-theoretic methods and their efficacy are demonstrated through illustrative numerical examples