A Lyapunov-Based Optimal Integral Finite-Time Tracking Control Approach for Asymmetric Nonholonomic Robotic Systems

This study suggests a control Lyapunov-based optimal integral terminal sliding mode control (ITSMC) technique for tracker design of asymmetric nonholonomic robotic systems in the existence of external disturbances. The design procedure is based on the control Lyapunov function (CLF) approach. Hence, the output tracking problem is solved by combining the ITSMC with optimal control. The CLF synthesizes a nonlinear optimal control input for the nominal system. Once the control system’s states lie far away from the operating point, it is activated to drive them toward the equilibrium point optimally. However, on the condition that the system perturbations are the main factor, the ITSMC would be designed to take over in the vicinity of the equilibrium point. Accordingly, the control goals, such as robustness and precise control, are warranted in the perturbed system. The usefulness of the suggested method is demonstrated with a wheeled mobile robot via a simulation study.

Global Optimal Stabilization of MT-HVDC Systems: Inverse Optimal Control Approach

The stabilization problem of multi-terminal high-voltage direct current (MT-HVDC) systems feeding constant power loads is addressed in this paper using an inverse optimal control (IOC). A hierarchical control structure using a convex optimization model in the secondary control stage and the IOC in the primary control stage is proposed to determine the set of references that allows the stabilization of the network under load variations. The main advantage of the IOC is that this control method ensures the closed-loop stability of the whole MT-HVDC system using a control Lyapunov function to determine the optimal control law. Numerical results in a reduced version of the CIGRE MT-HVDC system show the effectiveness of the IOC to stabilize the system under large disturbance scenarios, such as short-circuit events and topology changes. All the simulations are carried out in the MATLAB/Simulink environment.

Inverse optimal adaptive output feedback control of a class of Euler–Lagrange systems: A nonlinear filter based approach

In this paper, we present an inverse optimal tracking controller for a class of Euler–-Lagrange systems having uncertainties in their dynamical terms under the restriction that only the output state ( i.e. position for robotic systems) is available for measurement. Specifically, a nonlinear filter is used to generate a velocity substitute, then a controller formulation ensuring a globally asymptotically stable closed-loop system while minimizing a performance index despite the presence of parametric uncertainty, is proposed. The stability proof is established using a Lyapunov analysis of the system with proposed optimal output feedback controller. Inverse optimality is derived via designing a meaningful cost function utilizing the control Lyapunov function. Numerical simulations are presented to illustrate the viability and performance of the derived controller.

Robust Stabilization and Synchronization of a Novel Chaotic System with Input Saturation Constraints

In this paper, the robust stabilization and synchronization of a novel chaotic system are presented. First, a novel chaotic system is presented in which this system is realized by implementing a sigmoidal function to generate the chaotic behavior of this analyzed system. A bifurcation analysis is provided in which by varying three parameters of this chaotic system, the respective bifurcations plots are generated and evinced to analyze and verify when this system is in the stability region or in a chaotic regimen. Then, a robust controller is designed to drive the system variables from the chaotic regimen to stability so that these variables reach the equilibrium point in finite time. The robust controller is obtained by selecting an appropriate robust control Lyapunov function to obtain the resulting control law. For synchronization purposes, the novel chaotic system designed in this study is used as a drive and response system, considering that the error variable is implemented in a robust control Lyapunov function to drive this error variable to zero in finite time. In the control law design for stabilization and synchronization purposes, an extra state is provided to ensure that the saturated input sector condition must be mathematically tractable. A numerical experiment and simulation results are evinced, along with the respective discussion and conclusion.

Robust Inverse Optimal Control for a Boost Converter

The variability of renewable energies and their integration into the grid via power electronics demands the design of robust control algorithms. This work incorporates two techniques to ensure the stability of a boost converter through its state equations, implementing the inverse optimal control and the gain-scheduling technique for robust control settings. In such a way that, under a single adjustment, it is capable of damping different changes such as changes in the parameters, changes in the load, the input voltage, and the reference voltage. On the other hand, inverse optimal control is based on a discrete-time control Lyapunov function (CLF), and CLF candidate depends on fixed parameters that are selected to obtain the solution for inverse optimal control. Once these parameters have been found through heuristic or artificial intelligence methods, the new proposed methodology is capable of obtaining a robust optimal control scheme, without having to search for new parameters through other methods, since these are sometimes sensitive changes and many times the process of a new search is delayed. The results of the approach are simulated using Matlab, obtaining good performance of the proposed control under different operation conditions. Such simulations yielded errors of less than 1% based on the voltage reference, given the disturbances caused by changes in the input variables, system parameters, and changes in the reference. Thus, applying the new methodology, the stability of our system was preserved in all cases.

Adaptive Robust Tracking Control for Hybrid Models of Three-Dimensional Bipedal Robotic Walking Under Uncertainties

This paper introduces an adaptive robust trajectory tracking controller design to provably realize stable bipedal robotic walking under parametric and unmodeled uncertainties. Deriving such a controller is challenging mainly because of the highly complex bipedal walking dynamics that are hybrid and involve nonlinear, uncontrolled state-triggered jumps. The main contribution of the study is the synthesis of a continuous-phase adaptive robust tracking control law for hybrid models of bipedal robotic walking by incorporating the construction of multiple Lyapunov functions into the control Lyapunov function. The evolution of the Lyapunov function across the state-triggered jumps is explicitly analyzed to construct sufficient conditions that guide the proposed control design for provably guaranteeing the stability and tracking the performance of the hybrid system in the presence of uncertainties. Simulation results on fully actuated bipedal robotic walking validate the effectiveness of the proposed approach in walking stabilization under uncertainties.

Qualitative Analysis for Controllable Dynamical Systems: Stability with Control Lyapunov Functions

The present chapter focuses on some recent work on the qualitatively analysis of dynamical systems, namely stability, a powerful tool with multiple connected appliances. Among them, feedback is a powerful idea which is used extensively in natural and technological systems. In engineering, feedback has been rediscovered and patented many times in many different contexts. Stabilizing a dynamical system could be often easier if we approach controllable systems. When the dynamical system is in a controllable form, we can place bounds on its behavior by analyzing the improvement of the linear and nonlinear operators that describe the system. In this chapter it is analyzed how a control in a simple form, could influence the possibility to construct the so-called Control Lyapunov Function (CLF) in order to stabilize the dynamical system in study. The main idea is to test multiple cases, in order to get a rich information panel and to make easier the problem of finding a CLF, which is generally a difficult task. As applications, models from excitable media are chosen.

A Nonlinear Integral Backstepping Controller to Regulate the Voltage and Frequency of an Islanded Microgrid Inverter

The islanded operation mode of a microgrid system is usually affected by the system uncertainties, such as the load, source, and parameter variations. In such systems, the voltage and frequency must be regulated to maintain the power quality during islanded operation. As an approach to control the voltage and frequency, in this study, a decentralized nonlinear integral backstepping controller for the voltage source inverter used in an islanded microgrid is developed. First, the dynamical model of the inverter-based distribution generations (DGs) in microgrid system is developed. Subsequently, the model-based controller for the microgrid is built using dynamics of inverter-based DGs and Lyapunov theory, which could eliminate the voltage and frequency deviations in the system under different uncertainties. To ensure the system stability, a control Lyapunov function is adopted. Considering the influence of irradiations and other meteorological variables fluctuations a battery energy storage (BESS) is applied on the DC side to suppress the fluctuations of output power of DGs. Furthermore, the efficiency of the designed controller was validated through simulations in the MATLAB/Simulink environment under different scenarios and effectiveness of the proposed framework is further validated by real-time hardware in loop (HIL) experiments. In addition, the performance of the proposed controller is compared with a conventional backstepping (BS) controller. The comparison results demonstrate that the efficiency of the designed controller in terms of obtaining steady-state operating conditions is better than that of the BS controller.