Asymptotic Regulation Research Articles

Receding Horizon Control for Constrained Markovian Jump Linear Systems With Bounded Disturbance

This paper addresses the constrained receding horizon control scheme for a class of discrete-time Markovian jump linear systems with partly unknown transition probabilities and persistent bounded disturbances. The proposed method adopts paradigm that utilizes nominal closed-loop feedback controller plus an additional online optimized variable. Both the state feedback approach and the observer based approach are given. The obtained predictive controller guarantees constraint fulfillment and asymptotic state regulation in the mean square sense for all admissible disturbances. The system state and estimated state converge into a stochastic disturbance invariant set provided that the initial state and initial estimation error are feasible. A numerical example is given to verify the effectiveness of the proposed method.

Global Asymptotic Saturated PID Control for Robot Manipulators

This paper addresses the global asymptotic regulation of robot manipulators under input constraints, both with and without velocity measurements. It is proven that robot systems subject to bounded inputs can be globally asymptotically stabilized via a saturated proportional-integral-derivative (PID) control in agreement with Lyapunov's direct method and LaSalle's invariance principle. Advantages of the proposed controller include an absence of modeling parameters in the control law formulation and an ability to ensure actuator constraints are not breached. This is accomplished by selecting control gains a priori, removing the possibility of actuator failure due to excessive torque input levels. The effectiveness of the proposed approach is illustrated via simulations.

A simple PID control for asymptotic visual regulation of robot manipulators

AbstractThis paper addresses the asymptotic regulation problem of robot manipulators with a vision‐based feedback. A simple image‐based transpose Jacobian proportional‐integral‐derivative (PID) control is proposed. The closed‐loop system formed by the proposed PID control and robot system is shown to be asymptotically stable by using Lyapunov's direct method and LaSalle's invariance theorem. Advantages of the proposed control include the absence of dynamical model parameters in the control law formulation and the control gains are easily chosen according to simple inequalities including some well‐known bounds extracted from robot dynamics and kinematics. Simulations performed on a two degree‐of‐freedom manipulator are provided to illustrate the effectiveness of the proposed approach. Copyright © 2010 John Wiley & Sons, Ltd.

Robust generalized asymptotic regulation against non‐stationary sinusoidal disturbances with uncertain frequencies

AbstractAttenuation of sinusoidal disturbances with uncertain and arbitrarily time‐varying frequencies is considered in the form of a generalized asymptotic regulation problem. The disturbances are modeled as the outputs of a parameter‐dependent, unexcited and neutrally stable exogenous system that evolves from nonzero initial conditions. The problem is considered for a plant that depends partially on the uncertain parameters. Moreover, both the plant and the exogenous system are allowed to have dependence on another parameter vector that is measurable during online operation. The problem is then formulated as the synthesis of a controller that is scheduled on the measurable parameter in a way to guarantee robust internal stability and attenuate the disturbance according to a desired profile in steady state. The main result of the paper is a synthesis procedure based on a convex optimization problem, which is identified by a set of parameter‐dependent linear matrix inequalities and can be rendered tractable through standard relaxation schemes. It is also clarified how the transient behavior of the controller can be improved by some additional constraints. The order of the synthesized controller is equal to the order of the plant plus the order of the exogenous system. Copyright © 2010 John Wiley & Sons, Ltd.

On the Transient Response of a Nonlinear Output Regulator

In, Serrani, Isidori, and Marconi design an output feedback controller that achieves semiglobal output regulation for a class of minimum phase nonlinear systems. The controller has three components: an internal model to ensure asymptotic regulation, a high-gain partial state feedback controller to stabilize the augmented system of the plant and internal model, and a high-gain observer to implement the partial state feedback. In this note we show a property of the transient response of this controller. We consider an alternate controller that shares with the controller of the structure of high-gain partial state feedback and high-gain observer, but without internal model. Such controller can only achieve practical regulation. We show that when the controller and observer gains are large enough, the trajectories under the two controllers will be close to each other. Hence, the transient response of the controller of is not degraded by the inclusion of internal model. A similar transient response property is shown by Seshagiri and Khalil for the conditional servocompensator. Similarities and differences between the two designs are pointed out.

Robust adaptive control for nonholonomic systems with nonlinear parameterization

In this paper, an adaptive controller is designed for a class of nonholonomic systems in chained form with nonlinear parameterization. The robust adaptive control law is developed using parameter separation, state scaling and backstepping technique. Global asymptotic regulation of the closed-loop system states is achieved. The proposed control based switching strategy is proposed to overcome the uncontrollability problem associated with x 0 ( t 0 ) = 0 .

Robust Output Regulation of T--S Fuzzy Systems With Multiple Time-Varying State and Input Delays

This paper proposes a robust output regulator design for Takagi-Sugeno (T-S) fuzzy systems with uncertain time delays. For generalization of the control problem, we assume that there exist affine dynamics, unknown multiple time-varying delays in state and input, uncertain parameters, disturbance, and partial state feedback. Both continuous-time and discrete-time cases are considered in a unified theoretical derivation. Here, we introduce a memoryless fuzzy observer and a fuzzy integral compensator. In comparison with previous studies, the proposed scheme drops the need for coordinate transformation, calculation of the desired operational point, which is known state and input delays, and exact fuzzy modeling. The control result is asymptotic output regulation for systems without disturbance and guaranteed H infin performance for systems with disturbance. Moreover, a piecewise constant output regulation is achieved without controller redesign. In addition, the developed fuzzy regulator can be applied to both affine and nonaffine uncertain time-delay systems. Finally, numerical simulations are performed by using two typical time-delay systems to validate the expected performance.

Quaternion‐based visual servo control in the presence of camera calibration error

AbstractVisual servo control systems use information from images along with knowledge of the optic parameters (i.e. camera calibration) to position the camera relative to some viewed object. If there are inaccuracies in the camera calibration, then performance degradation and potentially unpredictable response from the visual servo control system may occur. Motivated by the desire to incorporate robustness to the camera calibration, different control methods have been developed. Previous adaptive/robust controllers (especially for six degree‐of‐freedom camera motion) rely heavily on properties of the rotation parameterization to formulate state estimates and a measurable closed‐loop error system. All of these results are based on the singular axis–angle parameterization. Motivated by the desire to express the rotation by a non‐singular parameterization, efforts in this paper address the question: Can state estimates and a measurable closed‐loop error system be crafted in terms of the quaternion parameterization when the camera calibration parameters are unknown? To answer this question, a contribution of this paper is the development of a robust controller and closed‐loop error system based on a new quaternion‐based estimate of the rotation error. A Lyapunov‐based analysis is provided which indicates that the controller yields asymptotic regulation of the rotation and translation error signals given a sufficient approximate of the camera calibration parameters. Simulation results are provided that illustrate the performance of the controller for a range of calibration uncertainty. Copyright © 2009 John Wiley & Sons, Ltd.

A New Neuro-FDS Definition for Indirect Adaptive Control of Unknown Nonlinear Systems Using a Method of Parameter Hopping

The indirect adaptive regulation of unknown nonlinear dynamical systems is considered in this paper. The method is based on a new neuro-fuzzy dynamical system (neuro-FDS) definition, which uses the concept of adaptive fuzzy systems (AFSs) operating in conjunction with high-order neural network functions (FHONNFs). Since the plant is considered unknown, we first propose its approximation by a special form of an FDS and then the fuzzy rules are approximated by appropriate HONNFs. Thus, the identification scheme leads up to a recurrent high-order neural network (RHONN), which however takes into account the fuzzy output partitions of the initial FDS. The proposed scheme does not require a priori experts' information on the number and type of input variable membership functions making it less vulnerable to initial design assumptions. Once the system is identified around an operation point, it is regulated to zero adaptively. Weight updating laws for the involved HONNFs are provided, which guarantee that both the identification error and the system states reach zero exponentially fast, while keeping all signals in the closed loop bounded. The existence of the control signal is always assured by introducing a novel method of parameter hopping, which is incorporated in the weight updating law. Simulations illustrate the potency of the method and comparisons with conventional approaches on benchmarking systems are given. Also, the applicability of the method is tested on a direct current (dc) motor system where it is shown that by following the proposed procedure one can obtain asymptotic regulation.

Pseudo-decentralized adaptive stabilization of large-scale feedforward nonlinear systems

In this paper, we propose a pseudo-decentralized adaptive control scheme for a class of large-scale feedforward nonlinear systems with unknown nonlinear effects within subsystems and unknown nonlinear interactions among subsystems. The local controller of each subsystem takes a nested saturation feedback, using the state of its own subsystem, and the saturation levels are tuned online in a switching manner via a set of switching logics, which requires some binary flag communication among subsystems. Global asymptotic regulation of the closed-loop states is achieved.

Asymptotic regulation of cascade systems with unknown control directions and nonlinear parameterization

A robust partial-state feedback asymptotic regulating control scheme is developed for a class of cascade systems with both nonlinear uncertainties and unknown control directions. A parameter separation technique is introduced to separate the time-varying uncertainty and the unmeasurable state from nonlinear functions. Then, the Nussbaum-type gain method together with the idea of changing supply functions is adopted in the design of a smooth partial-state regulator that can ensure all the signals of the closed-loop system are globally uniformly bounded. Especially, the system state asymptotically converges to zero. The design procedure is illustrated through an example and the simulation results show that the controller is feasible and effective.

Adaptive Robust Output Regulation of Uncertain Linear Periodic Systems

This paper considers the robust output regulation problem for parameterized families of periodic systems. To extend the solution of the output regulation problem to the periodic (or time-varying) setup, a classification of the immersion mappings based on various non-equivalent observability properties is derived. The connections between different canonical realizations of internal models that fully exploit such properties for robust and adaptive output regulation design in periodic systems are investigated. It is shown how non-minimal realizations of suitable periodic internal models are instrumental in achieving the possibility of performing adaptive redesign to deal with parameterized families of exosystem models. An important feature of the proposed solution is the fact that a persistence of excitation condition for the exogenous signals is not required for asymptotic regulation.

Generalized asymptotic regulation with guaranteed [formula omitted] performance: An LMI solution

A multi-objective controller synthesis problem is considered in which a set of generalized asymptotic regulation constraints are to be satisfied while also guaranteeing a desired level of performance measured in terms of the asymptotic variance of a performance output in response to a white noise random process with zero mean and identity covariance matrix. The generalized regulation constraints are expressed as bounds on the state-steady peak in response to disturbances generated by an anti-stable autonomous exogenous system with nonzero initial states. The controllers that guarantee these constraints can be realized by replicating the dynamics of the exogenous system within a certain structure formed by gain matrices, which are subject to convex constraints, and an accompanying controller with which the feedback loop is to be stabilized. Formulating the design of the accompanying controller in a way to guarantee the additional performance objective, the overall design is rendered tractable over a set of free variables, in terms of which the synthesis of a suitable controller is also outlined. The order of the controller is equal to the order of the plant plus the order of the exogenous system. By an adaptation of the developed techniques, a solution is also provided for the problem of generalized asymptotic regulation with suboptimal transient response.

Set-Point Regulation of LTI Nonminimum Phase Systems with a Single Positive Zero Using Two Sliding Lines

We deal with LTI nonminimum phase (NMP) systems which are difficult to control with conventional methods because of their inherent characteristics of undershoot. In such systems, reducing the undesirable undershoot phenomenon makes the response time of the systems much longer. Moreover, it is impossible to control the magnitude of undershoot in a direct way and to predict the response time. In this paper, we propose a novel two sliding mode control scheme which is capable of stably determining the magnitude of undershoot and thus the response time of NMP systems a priori. To do this, we introduce two sliding lines which are in charge of control in turn. One is used to stabilize the system and achieve asymptotic regulation eventually like the conventional sliding mode methods and the other to stably control the magnitude of undershoot from the beginning of control until the state meets the first sliding line. This control scheme will be proved to have an asymptotic regulation property. The computer simulation shows that the proposed control scheme is very effective and suitable for controlling the NMP systems compared with the conventional ones.

Indirect Adaptive Control of Unknown Nonlinear Systems with Parametric and Dynamic Uncertainties: A new Neuro-Fuzzy Method, Employing a Novel Approach of Parameter Hopping

Abstract Abstract The indirect adaptive regulation of unknown nonlinear dynamical systems under the presence of dynamic and parameter uncertainties, is considered in this paper. The method is based on a new Neuro-Fuzzy Dynamical Systems definition named Fuzzy-Recurrent High Order Neural Network (F-RHONN), which however takes into account the fuzzy output partitions of the initial fuzzy dynamical system (FDS) operating in conjunction with appropriate HONNFs, that approximates the fuzzy rules. The proposed scheme does not require a-priori experts’ information on the number and type of input variable membership functions making it less vulnerable to initial design assumptions. Once the system is identified around an operation point, it is regulated to zero adaptively. Weight updating laws for the involved HONNFs are provided, which guarantee that under the presence of ‘small’ dynamic uncertainties both the identification error and the system states reach zero exponentially fast, while keeping all signals in the closed loop bounded. The existence of the control signal is always assured by introducing a method of parameter hopping, which is incorporated in the weight updating law. The applicability is tested on the Lorenz model, where it is shown that by following the proposed procedure one can obtain asymptotic regulation quite well in the presence of unmodeled dynamics.

Lyapunov-Based Stabilization of MEMS Relays

In this paper, nonlinear stabilizers are introduced for voltage-controlled microelectromechanical system (MEMS) relays. The control constructions follow a Lyapunov approach and are based on a nonlinear dynamic model applicable to the two types of MEMS relays—electrostatic and electromagnetic. Two control schemes are presented with the objectives of avoiding pull-in during the microrelay closing and improving the transient response during the microrelay opening. First, an adaptive state feedback stabilizer is proposed to compensate for parametric uncertainty in all mechanical parameters and selected electrical parameters while ensuring asymptotic regulation of the electrode opening and closing. Next, a model-based observer/stabilizer is proposed to account for the lack of velocity measurements. Simulations demonstrate the performance of the two control schemes in comparison to the typical open-loop operation of the MEMS relay.

Synchronization of Animal-Inspired Multiple High-Lift Fins in an Underwater Vehicle Using Olivo–Cerebellar Dynamics

The development of neuroscience-based control methodologies and their integration with the high-lift unsteady hydrodynamics of control surfaces inspired by swimming and flying animals are the subjects of this paper. A biology-inspired rigid autonomous undersea vehicle called the biorobotic autonomous undersea vehicle (BAUV) has been developed at the Naval Undersea Warfare Center (NUWC), Newport, RI. The BAUV is equipped with six simultaneously rolling and pitching fins for generating large unsteady control forces for performing agile maneuvers. First, as an exploratory example, we introduce the van der Pol oscillator as an oscillatory controller for the BAUV and we describe experiments performed to examine the fin forces (thrust and lift) and electric power requirement, and to demonstrate the effectiveness of the oscillator's limit cycle property for disturbance rejection effectiveness. We then describe a BAUV control system that includes six inferior-olive (IO) neuron models for control of the pitch and roll motion of the six foils. These IO neurons exhibit limit cycle oscillation (LCO). For control of the BAUV, these IO neurons must oscillate in synchronism with specific relative phases. We present here four feedback linearizing control systems of varying complexity for control of the relative phases of the IO neurons. It is shown that each of the IO control systems accomplishes asymptotic regulation of the phases and thus enables the foils to produce the required control forces. The first controller has a global synchronization property, but the remaining controllers accomplish local synchronization. We present simulation results for tracking piecewise, time-varying phase angle commands as well as experimental results for control of the BAUV by IO neurons. The results show that with appropriate phasing of the fins, an optimal graceful gait of the BAUV is achieved where no untoward force or moment is present. An analog hardware version of the local controller with a cluster of six IO neurons has also been built, which allows five of the signals to rapidly synchronize to the reference, with or without prescribed phase shift, much like in the simulations. The designed controllers can be used in any platform or multivariate BAUV-like system requiring fast, accurate phase control. Laboratory test results for the phase synchronization of two servomotors (roll and pitch) using the designed analog hardware controller are also shown.

Adaptive Lyapunov-Based Control of a Robot and Mass–Spring System Undergoing an Impact Collision

The control of dynamic systems that undergo an impact collision is both theoretically challenging and of practical importance. An appeal of studying systems that undergo an impact is that short-duration effects such as high stresses, rapid dissipation of energy, and fast acceleration and deceleration may be achieved from low-energy sources. However, colliding systems present a difficult control challenge because the equations of motion are different when the system suddenly transitions from a noncontact state to a contact state. In this paper, an adaptive nonlinear controller is designed to regulate the states of two dynamic systems that collide. The academic example of a planar robot colliding with an unactuated mass-spring system is used to represent a broader class of such systems. The control objective is defined as the desire to command a robot to collide with an unactuated system and regulate the mass to a desired compressed state while compensating for the unknown constant system parameters. Lyapunov-based methods are used to develop a continuous adaptive controller that yields asymptotic regulation of the mass and robot links. It is interesting to note that one controller is responsible for achieving the control objective when the robot is in free motion (i.e., decoupled from the mass-spring system), when the systems collide, and when the system dynamics are coupled.

Passband Control of Lightly Damped Systems With Mode Separation

This paper deals with the regulation and stabilization of lightly damped systems under plant uncertainty. A controller consisting of a neural-network-based mode separator together with a modular passband tuning regulator is proposed. The mode separator generates the in-phase components of the plant utilized by the passband tuning regulator to maintain closed-loop stability and asymptotic regulation. This combined controller is robust and requires minimal plant information to operate. A synthesis procedure is outlined in this paper to summarize the design steps in a systematic manner. Finally, the application of the passband controller to the stabilization of a magnetic leadscrew is considered. Resonance is shown to be completely eliminated. The stabilization time of the transient response is also significantly reduced, confirming the feasibility of the controller.

On the Practical Stability of Incorporating Integral Compensation Into the Low-and-High Gain Control for a Class of Systems With Norm-Type Input Saturation

This paper studies the practical stability of incorporating integral compensation into the original low-and-high gain feedback law. The motivation for the incorporation is for achieving output regulation in the presence of constant disturbances without the use of a very large high-gain parameter required in the original approach. Due to numerical accuracy, the employment of very large high-gain parameters to eliminate steady-state error has the potential for inducing undesirable chattering effect on the control signal. A set of linear matrix inequalities is formulated in this study to obtain the related design parameters, by which the incorporation can achieve both the practical stabilization and asymptotic output regulation in the presence of input saturation and constant disturbances. Furthermore, the saturation of the control input can be shown to vanish in finite time during the process of regulation. Numerical examples are given to demonstrate the effectiveness of the proposed approach.