Observer-based event-triggered and set-theoretic neuro-adaptive controls for constrained uncertain systems

In this study, several new observer-based event-triggered and set-theoretic control schemes are presented to advance the state of the art in neuro-adaptive controls. In the first part, six new event-triggered neuro-adaptive control (ETNAC) schemes are presented for uncertain linear systems. These comprehensive designs offer flexibility to choose a design depending upon system performance requirements. Stability proofs for each scheme are presented and their performance is analyzed using benchmark examples. In the second part, the scope of the ETNAC is extended to uncertain nonlinear systems. It is applied to a case of precision formation flight of the microsatellites at the Sun-Earth/Moon L1 libration point. This dynamic system is selected to evaluate the performance of the ETNAC techniques in a setting that is highly nonlinear and chaotic in nature. Moreover, factors like restricted controls, response to uncertainties and jittering makes the controller design even trickier for maintaining a tight formation precision. Lyapunov function-based stability analysis and numerical results are presented. Note that most real-world systems involve constraints due to hardware limitations, disturbances, uncertainties, nonlinearities, and cannot always be efficiently controlled by using linearized models. To address all these issues simultaneously, a barrier Lyapunov function-based control architecture called the segregated prescribed performance guaranteeing neuro-adaptive control is developed and tested for the constrained uncertain nonlinear systems, in the third part. It guarantees strict performance that can be independently prescribed for each individual state and/or error signal of the given system. Furthermore, the proposed technique can identify unknown dynamics/uncertainties online and provides a way to regulate the control input --Abstract, page iv

Online Optimization of Switched LTI Systems Using Continuous-Time and Hybrid Accelerated Gradient Flows

This paper studies the design of feedback controllers that steer the output of a switched linear time-invariant system to the solution of a possibly time-varying optimization problem. The design of the feedback controllers is based on an online gradient descent method, and an online hybrid controller that can be seen as a regularized Nesterov's accelerated gradient method. Both of the proposed approaches accommodate output measurements of the plant, and are implemented in closed-loop with the switched dynamical system. By design, the controllers continuously steer the system output to an optimal trajectory implicitly defined by the time-varying optimization problem without requiring knowledge of exogenous inputs and disturbances. For cost functions that are smooth and satisfy the Polyak-Lojasiewicz inequality, we demonstrate that the online gradient descent controller ensures uniform global exponential stability when the time-scales of the plant and the controller are sufficiently separated and the switching signal of the plant is slow on the average. Under a strong convexity assumption, we also show that the online hybrid Nesterov's method guarantees tracking of optimal trajectories, and outperforms online controllers based on gradient descent. Interestingly, the proposed hybrid accelerated controller resolves the potential lack of robustness suffered by standard continuous-time accelerated gradient methods when coupled with a dynamical system. When the function is not strongly convex, we establish global practical asymptotic stability results for the accelerated method, and we unveil the existence of a trade-off between acceleration and exact convergence in online optimization problems with controllers using dynamic momentum. Our theoretical results are illustrated via different numerical examples

Adaptive Control

Adaptive control has been a remarkable field for industrial and academic research since 1950s. Since more and more adaptive algorithms are applied in various control applications, it is becoming very important for practical implementation. As it can be confirmed from the increasing number of conferences and journals on adaptive control topics, it is certain that the adaptive control is a significant guidance for technology development.The authors the chapters in this book are professionals in their areas and their recent research results are presented in this book which will also provide new ideas for improved performance of various control application problems

Switched dynamical systems: Transition model, qualitative theory, and advanced control

Ph.DDOCTOR OF PHILOSOPH

Development of Robust Control Strategies for Autonomous Underwater Vehicles

The resources of the energy and chemical balance in the ocean sustain mankind in many ways. Therefore, ocean exploration is an essential task that is accomplished by deploying Underwater Vehicles. An Underwater Vehicle with autonomy feature for its navigation and control is called Autonomous Underwater Vehicle (AUV). Among the task handled by an AUV, accurately positioning itself at a desired position with respect to the reference objects is called set-point control. Similarly, tracking of the reference trajectory is also another important task. Battery recharging of AUV, positioning with respect to underwater structure, cable, seabed, tracking of reference trajectory with desired accuracy and speed to avoid collision with the guiding vehicle in the last phase of docking are some significant applications where an AUV needs to perform the above tasks. Parametric uncertainties in AUV dynamics and actuator torque limitation necessitate to design robust control algorithms to achieve motion control objectives in the face of uncertainties. Sliding Mode Controller (SMC), H / μ synthesis, model based PID group controllers are some of the robust controllers which have been applied to AUV. But SMC suffers from less efficient tuning of its switching gains due to model parameters and noisy estimated acceleration states appearing in its control law. In addition, demand of high control effort due to high frequency chattering is another drawback of SMC. Furthermore, real-time implementation of H / μ synthesis controller based on its stability study is restricted due to use of linearly approximated dynamic model of an AUV, which hinders achieving robustness. Moreover, model based PID group controllers suffer from implementation complexities and exhibit poor transient and steady-state performances under parametric uncertainties. On the other hand model free Linear PID (LPID) has inherent problem of narrow convergence region, i.e.it can not ensure convergence of large initial error to zero. Additionally, it suffers from integrator-wind-up and subsequent saturation of actuator during the occurrence of large initial error. But LPID controller has inherent capability to cope up with the uncertainties. In view of addressing the above said problem, this work proposes wind-up free Nonlinear PID with Bounded Integral (BI) and Bounded Derivative (BD) for set-point control and combination of continuous SMC with Nonlinear PID with BI and BD namely SM-N-PID with BI and BD for trajectory tracking. Nonlinear functions are used for all P,I and D controllers (for both of set-point and tracking control) in addition to use of nonlinear tan hyperbolic function in SMC(for tracking only) such that torque demand from the controller can be kept within a limit. A direct Lyapunov analysis is pursued to prove stable motion of AUV. The efficacies of the proposed controllers are compared with other two controllers namely PD and N-PID without BI and BD for set-point control and PD plus Feedforward Compensation (FC) and SM-NPID without BI and BD for tracking control. Multiple AUVs cooperatively performing a mission offers several advantages over a single AUV in a non-cooperative manner; such as reliability and increased work efficiency, etc. Bandwidth limitation in acoustic medium possess challenges in designing cooperative motion control algorithm for multiple AUVs owing to the necessity of communication of sensors and actuator signals among AUVs. In literature, undirected graph based approach is used for control design under communication constraints and thus it is not suitable for large number of AUVs participating in a cooperative motion plan. Formation control is a popular cooperative motion control paradigm. This thesis models the formation as a minimally persistent directed graph and proposes control schemes for maintaining the distance constraints during the course of motion of entire formation. For formation control each AUV uses Sliding Mode Nonlinear PID controller with Bounded Integrator and Bounded Derivative. Direct Lyapunov stability analysis in the framework of input-to-state stability ensures the stable motion of formation while maintaining the desired distance constraints among the AUVs

Advances in PID Control

Since the foundation and up to the current state-of-the-art in control engineering, the problems of PID control steadily attract great attention of numerous researchers and remain inexhaustible source of new ideas for process of control system design and industrial applications. PID control effectiveness is usually caused by the nature of dynamical processes, conditioned that the majority of the industrial dynamical processes are well described by simple dynamic model of the first or second order. The efficacy of PID controllers vastly falls in case of complicated dynamics, nonlinearities, and varying parameters of the plant. This gives a pulse to further researches in the field of PID control. Consequently, the problems of advanced PID control system design methodologies, rules of adaptive PID control, self-tuning procedures, and particularly robustness and transient performance for nonlinear systems, still remain as the areas of the lively interests for many scientists and researchers at the present time. The recent research results presented in this book provide new ideas for improved performance of PID control applications