Observer-based Output Feedback Control Law Research Articles

Spatiotemporally asynchronous sampled-data control of a linear parabolic PDE on a hypercube

This paper employs the observer-based output feedback control technique to deal with the problem of spatiotemporally asynchronous sampled-data control for a linear parabolic PDE on a hypercube. By the spatiotemporally asynchronous sampled-data observation outputs, an observer-based output feedback control law is constructed, where the sampling interval in time is bounded. By constructing an appropriate Lyapunov–Krasovskii functional candidate and applying a weighted Poincaré–Wirtinger inequality on a hypercube, it is shown under a sufficient condition presented in terms of standard linear matrix inequalities that the suggested spatiotemporally asynchronous sampled-data control law asymptotically stabilises the PDE in the spatial norm but its convergence speed can be regulated by a known constant. Moreover, both open-loop and closed-loop well-posedness analysis are done within the framework of semi-group. Finally, numerical simulation results are presented to support the proposed design method.

Zonotopic Kalman filtering for stability augmentation and flight envelope estimation

This article introduces a novel methodology based on zonotopic Kalman filtering for stabilizing attitude dynamics and estimating flight envelopes of an unmanned helicopter via an observer-based (output) feedback control law and a reachability analysis, respectively. The helicopter dynamics is represented by a linear state-space model, based on which the feedback control law is designed. Since not all state variables are measurable, state information is acquired by applying a zonotopic Kalman filter to yield sets of state-variable estimates of the helicopter in terms of zonotopes. Not only are the resulting zonotopes used for the observer-based feedback control, but also for estimating the flight envelopes of the helicopter based on the reachability analysis. This approach is useful for enhancing pilot’s awareness about dynamic responses of the helicopter, which may undergo unsafe flight conditions due to actuator faults triggered by undesirable perturbations. The efficacy of the proposed methodology is demonstrated via an example, where we also expose the benefits of applying the zonotopic Kalman filter as compared with an ordinary stochastic Kalman filter.

Output feedback compensation to state and measurement delays for a first-order hyperbolic PIDE with recycle

This paper develops a novel observer-based output-feedback control law for a class of interconnected first-order hyperbolic partial integral differential equations (PIDEs) with in-domain, non-local coupling terms and measurement delay compensation. A transport PDE is introduced to account for in-domain recycle delay which results in an extended spatial domain with the PIDE and transport PDE being cascaded. Since standard backstepping approach cannot be applied, an affine Volterra integral transform is introduced which allows for the construction of a boundary controller for the PIDE and delay compensation. An observer backstepping transformation containing four kernels is realized, reconstructing the states throughout the delayed measurement. By the use of the backstepping method, a set of coupled kernel equations where one of the kernels has two boundary conditions is established. The existence and invertibility for the control and observer transformations are proved and the finite-time stability for the output system is established while results are illustrated by numerical simulations.

Laser Sintering Control for Metal Additive Manufacturing by PDE Backstepping

Metal additive manufacturing (AM) has been intensively advanced due to numerous industrial applications, such as automobiles, aerospace, consumer electronics, and medical devices. The dynamics of the melt pool via laser sintering for metal AM has been studied by means of the thermodynamic phase change model known as the “Stefan problem”. In this article, we develop a control design for the laser power to drive the depth of the melt pool to the desired set point. The governing equation is described by a partial differential equation (PDE) defined on a time-varying spatial domain, which is dependent on the PDE state, and the optical penetration of the laser energy affects the PDE dynamics in the domain as well as at the surface boundary. First, we design the full-state feedback control law utilizing the entire spatial profile of the temperature in the melt pool and the moving interface position. The closed-loop system is proven to satisfy some conditions to validate the physical model, and its origin is shown to be exponentially stable. Next, we propose an observer-based output feedback control law by reconstructing the temperature profile with the availability of only the measured interface position and prove the analogous properties of the closed-loop system. Numerical simulation for a controller designed on a single-phase Stefan model is conducted on a more complex and realistic two-phase Stefan model, which incorporates the cooling effect from the solid phase. In addition, a bias in the interface location measurement is considered. The numerical results illustrate the robustness of the proposed feedback. By lowering the initial temperature in the solid and by increasing the interface sensor bias to more extreme levels, which leads to the controller’s failure (where the failure is exhibited through the entire metal freezing and the melt pool disappearing), we explore the limits of how much uncertainty our control law can handle.

Target tracking for non-identical high-order networks based on reduced-order observers

ABSTRACTIn this paper, target tracking for non-identical high-order networks is presented under the digraph network topology. The target agent has different dimensions with the followers. We first address a distributed dynamic state feedback control law to solve the output tracking problem. Then a reduced-order observer is designed, and an observer-based dynamic output feedback control law is given for the case that the states of the agents are not fully measurable. Finally, some simulation results are given to illustrate the validity of the theoretical results.

Nonlinear bilateral output-feedback control for a class of viscous Hamilton–Jacobi PDEs

We tackle the boundary control and estimation problems for a class of viscous Hamilton–Jacobi PDEs, considering bilateral actuation and sensing, i.e., at the two boundaries of a 1-D spatial domain. We first solve the nonlinear trajectory generation problem for this type of PDEs, providing the necessary feedforward actions at both boundaries. We then design an observer-based output-feedback control law, which consists of two main elements—a nonlinear observer that is constructed utilizing measurements from both boundaries and state-feedback laws, which are employed at the two boundary ends. All of our designs are explicit since they are constructed interlacing a feedback linearizing transformation with backstepping. Due to the fact that the linearizing transformation is locally invertible, only a regional stability result is established, combining this transformation with backstepping, suitably formulated to handle the case of bilateral actuation and sensing. We illustrate the developed methodologies via application to traffic flow control and we present consistent simulation results.

Semi-global containment control of discrete-time linear systems with actuator position and rate saturation

In this paper, we study semi-global containment control problem for a multi-agent system in the presence of multiple leader agents. We describe the dynamics of each follower agent in multi-agent system by a general discrete-time linear system subject to both actuator position and rate saturation. By using low gain approach, we construct both a linear state feedback control law and an observer-based output feedback control law for each follower agent. Under some standard assumptions, we provide a sufficient condition to guarantee that the states of follower agents converge to the convex hull formed by the leader agents asymptotically. Finally, we illustrate the theoretical results by numerical simulation results.

Axial Vibration Suppression in a Partial Differential Equation Model of Ascending Mining Cable Elevator

Lifting up a cage with miners via a mining cable causes axial vibrations of the cable. These vibration dynamics can be described by a coupled wave partial differential equation-ordinary differential equation (PDE-ODE) system with a Neumann interconnection on a time-varying spatial domain. Such a system is actuated not at the moving cage boundary, but at a separate fixed boundary where a hydraulic actuator acts on a floating sheave. In this paper, an observer-based output-feedback control law for the suppression of the axial vibration in the varying-length mining cable is designed by the backstepping method. The control law is obtained through the estimated distributed vibration displacements constructed via available boundary measurements. The exponential stability of the closed-loop system with the output-feedback control law is shown by Lyapunov analysis. The performance of the proposed controller is investigated via numerical simulation, which illustrates the effective vibration suppression with the fast convergence of the observer error.

Indirect Adaptive Fuzzy Supervisory Control with State Observer for Unknown Nonlinear Time Delay System

This paper proposes an indirect adaptive fuzzy neural network (FNN) controller with state observer and supervisory controller for a class of uncertain nonlinear dynamic time delay systems. First, the approximate function of unknown time delay system is inferred by the adaptive time delay FNN system. Next, a state observer is designed to estimate the unknown system states and the indirect adaptive fuzzy controller is constructed. Finally, the closed loop controller is obtained by incorporating the supervisory controller with the indirect adaptive fuzzy controller. Therefore, if the system tends to unstable, i.e., error dynamics is larger than a prescribed constraint which is determined by designer, the supervisory controller will activate to force the state to be stable. The free parameters of the indirect adaptive FNN controller can be tuned online by observer-based output feedback control law and adaptive laws by means of Lyapunov stability criterion. The resulting simulation example shows that the performance of nonlinear time delay chaotic system is fully tracking the reference trajectory. Meanwhile, simulation results show that the adaptive control effort of the proposed control scheme is much less due to the assist of the supervisory controller.

Nonlinear Local Stabilization of a Viscous Hamilton-Jacobi PDE

We consider the boundary stabilization problem of the non-uniform equilibrium profiles of a viscous Hamilton-Jacobi (HJ) Partial Differential Equation (PDE) with parabolic concave Hamiltonian. We design a nonlinear full-state feedback control law, assuming Neumann actuation, which achieves an arbitrary rate of convergence to the equilibrium. Our design is based on a feedback linearizing transformation which is locally invertible. We prove local exponential stability of the closed-loop system in the $H^{1} $ norm, by constructing a Lyapunov functional, and provide an estimate of the region of attraction. We design an observer-based output-feedback control law, by constructing a nonlinear observer, using only boundary measurements. We illustrate the results on a benchmark example computed numerically.

Adaptive hybrid intelligent control for uncertain nonlinear dynamical systems

A new hybrid direct/indirect adaptive fuzzy neural network (FNN) controller with a state observer and supervisory controller for a class of uncertain nonlinear dynamic systems is developed in this paper. The hybrid adaptive FNN controller, the free parameters of which can be tuned on-line by an observer-based output feedback control law and adaptive law, is a combination of direct and indirect adaptive FNN controllers. A weighting factor, which can be adjusted by the tradeoff between plant knowledge and control knowledge, is adopted to sum together the control efforts from indirect adaptive FNN controller and direct adaptive FNN controller. Furthermore, a supervisory controller is appended into the FNN controller to force the state to be within the constraint set. Therefore, if the FNN controller cannot maintain the stability, the supervisory controller starts working to guarantee stability. On the other hand, if the FNN controller works well, the supervisory controller will be deactivated. The overall adaptive scheme guarantees the global stability of the resulting closed-loop system in the sense that all signals involved are uniformly bounded. Two nonlinear systems, namely, inverted pendulum system and Chua's (1989) chaotic circuit, are fully illustrated to track sinusoidal signals. The resulting hybrid direct/indirect FNN control systems show better performances, i.e., tracking error and control effort can be made smaller and it is more flexible during the design process.

Direct adaptive fuzzy-neural control with state observer and supervisory controller for unknown nonlinear dynamical systems

In this paper, an observer-based direct adaptive fuzzy-neural network (FNN) controller with supervisory mode for a certain class of high order unknown nonlinear dynamical system is presented. The direct adaptive control (DAC) has the advantage of less design effort by not using FNN to model the plant. By using an observer-based output feedback control law and adaptive law, the free parameters of the adaptive FNN controller can be tuned on-line based on the Lyapunov synthesis approach. A supervisory controller is appended into the FNN controller to force the state to be within the constraint set. Therefore, if the FNN controller cannot maintain the stability, the supervisory controller starts working to guarantee stability. On the other hand, if the FNN controller works well, the supervisory controller will be de-activated. The overall adaptive scheme guarantees the global stability of the resulting closed-loop system in the sense that all signals involved are uniformly bounded. Simulation results also show that our initial control effort is much less than those in previous works, while preserving the tracking performance.

Observer-based adaptive fuzzy-neural control for unknown nonlinear dynamical systems

In this paper, an observer-based adaptive fuzzy-neural controller for a class of unknown nonlinear dynamical systems is developed. The observer-based output feedback control law and update law to tune on-line the weighting factors of the adaptive fuzzy-neural controller are derived. The total states of the nonlinear system are not assumed to be available for measurement. Also, the unknown nonlinearities of the nonlinear dynamical systems are not restricted to the system output only. The overall adaptive scheme guarantees that all signals involved are bounded. Simulation results demonstrate the applicability of the proposed method in order to achieve desired performance.

Design of robust reliable H∞output feedback control for a class of uncertain linear systems with sensor failure

The problem of robust reliable H∞ output feedback controller design is investigated for uncertain linear systems with sensor failures within a prespecified subset of sensors. The uncertainty considered here is time-varying norm-bounded parameter uncertainty in the state matrix. The output of a faulty sensor is assumed to be any arbitrary energy-bounded signal. An observer-based output feedback control design is presented which stabilizes the plant and guarantees an H∞ norm bound on attenuation of augmented disturbances, for all admissible uncertainties as well as sensor failures. The construction of the observer-based output feedback control law requires the positive-definite solutions of two algebraic Riccati equations. The result can be regarded as an extension of existing results on robust H∞ control and reliable H∞ control of uncertain linear systems.

Robust Observer-Based Control of Large Flexible Structures

This paper considers robust stabilization of the spillover phenomenon of large flexible structures. New frequency domain robustness measures for a large flexible structure system controlled by an observer-based compensator is derived via a state-space framework. In the present approach, control and observation spillover are viewed as parametric perturbations, and the total spillover (combination of control and observation spillover) is treated as the unmodeled dynamics. A robust observer-based output feedback control law, obtained by solving two algebraic Riccati equations, is provided. Finally, a simply supported beam example is included to illustrate the application.