Composite Learning Control With Application to Inverted Pendulums

Composite adaptive control (CAC) that integrates direct and indirect adaptive control techniques can achieve smaller tracking errors and faster parameter convergence compared with direct and indirect adaptive control techniques. However, the condition of persistent excitation (PE) still has to be satisfied to guarantee parameter convergence in CAC. This paper proposes a novel model reference composite learning control (MRCLC) strategy for a class of affine nonlinear systems with parametric uncertainties to guarantee parameter convergence without the PE condition. In the composite learning, an integral during a moving-time window is utilized to construct a prediction error, a linear filter is applied to alleviate the derivation of plant states, and both the tracking error and the prediction error are applied to update parametric estimates. It is proven that the closed-loop system achieves global exponential-like stability under interval excitation rather than PE of regression functions. The effectiveness of the proposed MRCLC has been verified by the application to an inverted pendulum control problem.Comment: 5 pages, 6 figures, conference submissio

Adaptive control for time-varying systems: congelation and interconnection

This thesis investigates the adaptive control problem for systems with time-varying parameters. Two concepts are developed and exploited throughout the thesis: the congelation of variables, and the active nodes. The thesis first revisits the classical adaptive schemes and explains the challenges brought by the presence of time-varying parameters. Then, the concept of congelation of variables is introduced and its use in combinations with passivity-based, immersion-and-invariant, and identification-based adaptive schemes are discussed. As the congelation of variables method introduces additional interconnection in the closed-loop system, a framework for small-gain-like control synthesis for interconnected systems is needed.\vspace{2ex} To this end, the thesis proceeds by introducing the notion of active nodes. This is instrumental to show that as long as a class of node systems that possess adjustable damping parameters, that is the active nodes, satisfy certain graph-theoretic conditions, the desired small-gain-like property for the overall system can be enforced via tuning these adjustable parameters. Such conditions for interconnected systems with quadratic, nonlinear, and linearly parametrized supply rates, respectively, are elaborated from the analysis and control synthesis perspectives. The placement and the computation/adaptation of the damping parameters are also discussed. Following the introduction of these two fundamental tools, the thesis proceeds by discussing state-feedback designs for a class of lower-triangular nonlinear systems. The backstepping technique and the congelation of variables method are combined for passivity-based, immersion-and-invariance, and identification-based schemes. The notion of active nodes is exploited to yield simple and systematic proofs. Based on the results established for lower-triangular systems, the thesis continues to investigate output-feedback adaptive control problems. An immersion-and-invariance scheme for single-input single-output linear systems and a passivity-based scheme for nonlinear systems in observer form are proposed. The proof and interpretation of these results are also based on the notion of active nodes. The simulation results show that the adaptive control schemes proposed in the thesis have superior performance when compared with the classical schemes in the presence of time-varying parameters. Finally, the thesis studies two applications of the theoretical results proposed. The servo control problem for serial elastic actuators, and the disease control problem for interconnected settlements. The discussions show that these problems can be solved efficiently using the framework provided by the thesis.Open Acces

Adaptive, Neural and Robust Control of Wing-Rock and Aeroelastic System

Modern aircraft exhibit wing-rock phenomenon and aeroelastic instability. Wingrock (roll single degree of freedom motion) and aeroelastic systems\u27 (two degrees of freedom) behavior are described by complex nonlinear differential equations. The nonlinearities in the dynamics of these systems give rise to limit cycle oscillations beyond critical speed of aircraft. The onset of wing-rock and aeroelastic instability limits the performance of aircraft and can even lead to catastrophic consequences. Therefore, control of wing-rock motion and stabilization of aeroelastic systems are important. In the past, several studies have been made and experimental and analytical results have been obtained to explain the wing-rock and aeroelastic phenomena in wind-tunnel tests, and also control systems have been derived. Motivation for this research is the importance of flying aircraft in a large flight envelope in which complex uncertain aerodynamic nonlinearities appear, causing instabilities and flutter in the aircraft wings. For the control of wing-rock motion and the stabilization of aeroelastic instabilities, new control systems are designed. Because modeling of nonlinear dynamics of wing-rock motion and aeroelastic systems are imprecise, the control algorithms must be insensitive to model uncertainties. Apparently control theory for deterministic systems is not applicable to uncertain systems. For the stabilization of wing-rock, two non-certainity equivalent adaptive (NCEA) laws are designed. The first control system includes a finite form realization of a speed-gradient adaptation law, and the second controller is based on the Immersion and Invariance (I&I) theory. For the nonlinear multi-input multi-output (MIMO) aeroelastic systems, equipped with leading- and trailing-edge control surfaces, four distinct control systems are designed. First, a Chebyshev neural adaptive control law is derived for the suppression of limit cycle oscillations (LCOs) of the prototypical wing. For this derivation SDU decomposition of the high-frequency constant gain matrix is utilized for obtaining a singularity free controller. Then for a multi-input aeroelastic system with state dependent input matrix, a higher-order robust sliding mode control law for finite-time stabilization is derived. This is followed by the design of a suboptimal controller based on the state-dependent Riccati equation (SDRE) method. Finally, a suboptimal control law is designed for the control of the aerolelastic system, based dierential game theory. In this approach, the wind gust is treated as an adversary which tries to destabilize system. These control algorithms are simulated using MATLAB and SIMULINK to verify their performance. Results show that the designed controllers are effective in suppressing the limit cycle oscillations

Nonlinear energy-based control of soft continuum pneumatic manipulators

This paper investigates the model-based nonlinear control of a class of soft continuum pneumatic manipulators that bend due to pressurization of their internal chambers and that operate in the presence of disturbances. A port-Hamiltonian formulation is employed to describe the closed loop system dynamics, which includes the pressure dynamics of the pneumatic actuation, and new nonlinear control laws are constructed with an energy-based approach. In particular, a multi-step design procedure is outlined for soft continuum manipulators operating on a plane and in 3D space. The resulting nonlinear control laws are combined with adaptive observers to compensate the effect of unknown disturbances and model uncertainties. Stability conditions are investigated with a Lyapunov approach, and the effect of the tuning parameters is discussed. For comparison purposes, a different control law constructed with a backstepping procedure is also presented. The effectiveness of the control strategy is demonstrated with simulations and with experiments on a prototype. To this end, a needle valve operated by a servo motor is employed instead of more sophisticated digital pressure regulators. The proposed controllers effectively regulate the tip rotation of the prototype, while preventing vibrations and compensating the effects of disturbances, and demonstrate improved performance compared to the backstepping alternative and to a PID algorithm

Onboard control, tracking and navigation for autonomous systems

To operate effectively and safely, autonomous systems must be able to navigate complex environments, precisely control their attitude, accurately estimate their own states and make real-time decisions. A new adaptive controller is designed for attitude tracking control of rigid spacecraft with inertia uncertainties and full state feedback of attitude and angular rate. The controller preserves the proportional-derivative plus feedforward (PD+) structure but introduces time varying feedback gains, wherein the desired attitude state is represented by quaternions. Stable asymptotic tracking of the desired reference trajectories is guaranteed without any further restrictions upon the initial conditions, reference trajectories or any requirement for a priori availability of bounds upon the inertia matrix. The onboard estimation of the angular velocity of a spacecraft using Rate-integrating Gyroscopes (RIGs) is considered next. RIGs provide measurements of angular displacement which need to a low pass filter or observer to obtain angular velocity of the system. A continuous time observer is proposed which estimates angular velocity using the RIG measurements and achieves exponential convergence, while asymptotic convergence is guaranteed for the adaptive inertia observer. Unlike conventional certainty equivalence methods, a novel adaptation update law is proposed with additional control knobs changing with the attitude states. The final part of the dissertation deals with the Simultaneous Localization and Mapping (SLAM) problem. Estimating the location of a robot along with the position of the surrounding features on a map can be done onboard recursively with a simple Extended Kalman Filter (EKF-SLAM), but has higher chances of divergence and inconsistency. The robocentric SLAM method transforms the map of features to a local reference frame centered at the robot's position, leading to reduced inconsistency due to lower linearization errors in the update function. Improvements to the robocentric SLAM methods are suggested in the form of addition of second order terms to the linear propagation step and elimination of the composition step by transforming the feature maps before every update step. These modifications provide better filter consistency and prevent divergence in cases which were previously not possible.Aerospace Engineerin

On self-learning mechanism for the output regulation of second-order affine nonlinear systems

This paper studies global robust output regulation of second-order nonlinear systems with input disturbances that encompass the fully-actuated Euler-Lagrange systems. We assume the availability of relative output (w.r.t. a family of reference signals) and output derivative measurements. Based on a specific separation principle and self learning mechanism, we develop an internal model-based controller that does not require apriori knowledge of reference and disturbance signals and it only assumes that the kernels of these signals are a family of exosystems with unknown parameters (e.g., amplitudes, frequencies or time periods). The proposed control framework has a self-learning mechanism that extricates itself from requiring absolute position measurement nor precise knowledge of the feedforward kernel signals. By requiring the high-level task/trajectory planner to use the same class of kernels in constraining the trajectories, the proposed low-level controller is able to learn the desired trajectories, to suppress the disturbance signals, and to adapt itself to the uncertain plant parameters. The framework enables a plug-and-play control mechanism in both levels of control