Guarantee Parameter Convergence Research Articles

Composite adaptive attitude control for combined spacecraft with inertia uncertainties

This paper examines the attitude control problem of the combined spacecraft subject to inertia uncertainties. A composite adaptive finite-time control scheme with guaranteed parameter convergence is proposed to address this challenging problem, in the absence of persistent excitation. As a stepping stone, the attitude dynamics of the combined spacecraft is first established with explicit consideration of the center-of-mass variation and thruster reconfiguration. Then, a composite adaptive finite-time controller is developed based on a constructive time-varying sliding manifold, and in particular, the concurrent learning technique is used in conjunction with the dynamic regressor extension and mixing procedure to achieve parameter convergence under finite excitation that is strictly weaker than the persistent excitation. Lyapunov stability analysis shows that the derived adaptive controller can simultaneously guarantee finite-time convergence of the attitude tracking and parameter estimation errors; moreover, its robustness against inertia variations and external disturbances is also analyzed. Finally, a set of numerical simulations under ideal and practical scenarios are performed to validate the effectiveness and outperformance of the proposed method.

Composite Adaptive Control for Anti-Unwinding Attitude Maneuvers: An Exponential Stability Result Without Persistent Excitation

This paper provides an exponential stability result for the adaptive anti-unwinding attitude tracking problem of a rigid body with uncertain inertia parameters, without the need for a persistent excitation (PE) condition. Specifically, a composite adaptive control scheme with guaranteed parameter convergence is proposed by integrating the dynamic regressor extension and mixing (DREM) technique into the dynamically scaled immersion and invariance adaptive control framework, wherein we modify the scaling factor so that the algorithm design does not involve any dynamic gains. To avoid the unwinding problem, a barrier function is introduced as the attitude error function, along with the establishment of two key algebraic properties for exponential stability analysis. Aiding by an linear time-varying filter, the scalar regressor of DREM is extended to generate an exciting counterpart. In this manner, the derived controller is shown to permit closed-loop exponential stability under a strictly weaker interval excitation condition than PE, in the sense that both the output-tracking and parameter estimation errors exponentially converge to zero. Furthermore, the composite adaptive law is also augmented to achieve finite/fixed-time parameter convergence in a time-synchronized manner. Simulation results are presented to verify our theoretical findings.

Combined Cooperative Adaptive Cruise Control using Collective Initial Excitation based Distributed Parameter Estimator

In cooperative adaptive cruise control (CACC), autonomous vehicles are grouped into a string of platoon and, the main objective is to automatically adapt their speed using on-board sensors and communication with the preceding vehicle to maintain a desired inter-vehicle distance. Cruise control is achieved in the presence of parametric uncertainty in the vehicle dynamics using principles of adaptive control. This work proposes a novel combined CACC strategy for an uncertain homogeneous platoon with guaranteed parameter convergence and asymptotic string stability. A novel distributed consensus-based parameter estimator is proposed in conjunction with a model reference adaptive control (MRAC) algorithm using a direct control-gain update law. The algorithm ensures exponential parameter estimation error convergence to zero as well as asymptotic convergence of tracking-error to zero. Conventional CACC protocols require a condition of persistence of excitation (PE) for parameter convergence, which is required for better transient performance in converging to a string stable configuration. The PE condition is highly restrictive in the context of cruise control since velocity profiles which are demanded in the platoon model do not typically satisfy the PE condition. In contrast, the proposed scheme can ensure parameter convergence under a significantly milder condition, coined as collective initial excitation (C-IE). The C-IE condition is an extension of the concept of initial excitation (IE), which is recently proposed in the context of adaptive control of single agent system. Unlike IE, the C-IE condition caters to distributed estimation in the context of multi-agent systems. As far as the authors are aware, this is the first work on CACC framework, which ensures exponential convergence of parameter estimation error of each vehicle under the mild condition of C-IE, which further leads to asymptotic convergence of the entire vehicle platoon to a string stable configuration. Simulation study dictates that the proposed CACC architecture outperforms the existing CACC algorithms in terms of tracking and estimation performance.

Novel model reference adaptive control architecture using semi‐initial excitation‐based switched parameter estimator

SummaryThis paper is a generalization of the recently developed techniques of initial excitation (IE)–based adaptive control with an introduction to the definition of semi‐initial excitation (semi‐IE), a still more relaxed notion than IE. Classical adaptive controllers typically ensure Lyapunov stability of the extended error dynamics (tracking error + parameter estimation error) and asymptotic tracking, while requiring a stringent condition of persistence of excitation (PE) for parameter convergence. Of late, the authors have proposed a new adaptive control architecture, which guarantees parameter convergence under the online‐verifiable IE condition leading to exponential stability of the extended error dynamics. In earlier works, it has been established that the IE condition is significantly milder than the classical PE condition. The current work further slackens the excitation condition by proposing the concept of semi‐IE. The proposed adaptive controller is proved to ensure convergence of the parameter estimation error to a lower‐dimensional manifold under the weaker semi‐IE condition, while the stronger condition of IE guarantees convergence of the parameter estimation error to zero. The designed algorithm is shown to improve transient response of tracking error sufficiently in contrast to conventional adaptive controllers.

Robust MPC with recursive model update

Robust constrained control of linear systems with parametric uncertainty and additive disturbance is addressed. The main contribution is the introduction of a mathematically rigorous and computationally tractable framework for stabilizing model predictive control with online parameter estimation to improve performance and reduce conservatism. Requirements for closed-loop stability and provable constraint satisfaction are considered separately, resulting in the use of online set-membership system identification combined with homothetic prediction tubes for robust constraint satisfaction, and an H∞ optimal point estimate of the unknown parameters to achieve a finite closed-loop gain from the disturbance to the state. Extensions to time-varying parameters and persistently exciting inputs to guarantee parameter convergence are presented. A numerical example illustrates the proven properties and efficacy of the approach.

Direct Adaptive Optimal Control for Uncertain Continuous-Time LTI Systems Without Persistence of Excitation

This brief presents a novel direct adaptive optimal controller design for uncertain continuous-time linear time-invariant systems. The optimal gain parameter, obtained from the Riccati equation, is continuously estimated without using knowledge of the system dynamics, rather information rich past, and current data along the system trajectory is used for parameter estimation. This approach guarantees parameter convergence to the close neighborhood of the optimal controller by relaxing the restrictive persistence of excitation condition, typically required for achieving parameter convergence in approximate/adaptive optimal control methods. A Lyapunov-based analysis establishes the uniformly ultimately bounded stability of the designed controller. Further a simulation example demonstrates the efficacy of the proposed result.

Integral concurrent learning: Adaptive control with parameter convergence using finite excitation

SummaryConcurrent learning (CL) is a recently developed adaptive update scheme that can be used to guarantee parameter convergence without requiring persistent excitation. However, this technique requires knowledge of state derivatives, which are usually not directly sensed and therefore must be estimated. A novel integral CL method is developed in this paper that removes the need to estimate state derivatives while maintaining parameter convergence properties. Data recorded online is exploited in the adaptive update law, and numerical integration is used to circumvent the need for state derivatives. The novel adaptive update law results in negative definite parameter error terms in the Lyapunov analysis, provided an online‐verifiable finite excitation condition is satisfied. A Monte Carlo simulation illustrates improved robustness to noise compared to the traditional derivative formulation. The result is also extended to Euler‐Lagrange systems, and simulations on a two‐link planar robot demonstrate the improved performance compared to gradient‐based adaptation laws.

Composite Adaptive Control of Uncertain Euler‐Lagrange Systems with Parameter Convergence without PE Condition

AbstractThis work proposes a novel composite adaptive controller for uncertain Euler‐Lagrange (EL) systems. The composite adaptive law is strategically designed to be proportional to the parameter estimation error in addition to the tracking error, leading to parameter convergence. Unlike conventional adaptive control laws which require the regressor function to be persistently exciting (PE) for parameter convergence, the proposed method guarantees parameter convergence from a milder initially exciting (IE) condition on the regressor. The IE condition is significantly less restrictive than PE, since it does not rely on the future values of the signal and that it can be verified online. The proposed adaptive controller ensures exponential convergence of the tracking and the parameter estimation errors to zero once the sufficient IE condition is met. Simulation results corroborate the efficacy of the proposed technique and also establishes it's robustness property in the presence of unmodeled bounded disturbance.

Composite learning robot control with guaranteed parameter convergence

Parameter convergence is desirable in adaptive control as it enhances the overall stability and robustness properties of the closed-loop system. However, a stringent condition termed persistent excitation (PE) must be satisfied to guarantee parameter convergence in the conventional adaptive control. This paper provides the first result of parameter convergence without the PE condition for adaptive control of a general class of robotic systems. More specifically, we develop a composite learning robot control (CLRC) strategy to achieve fast and accurate parameter estimation under a condition termed interval excitation (IE) which is much weaker than the PE condition. In the composite learning, a time-interval integral of a filtered regressor is utilized to construct a prediction error such that the time derivation of plant states is not necessary, and both the prediction error and a filtered tracking error are employed to update the parameter estimate. The closed-loop system is proven to be globally exponentially stable under the IE condition. Robustness against external disturbances of the CLRC is analyzed in the Lyapunov sense. An illustrative example shows the effectiveness and superiority of the proposed approach.

Combined MRAC for Unknown MIMO LTI Systems With Parameter Convergence

This work proposes a novel combined model reference adaptive controller (MRAC) for unknown multi input multi output (MIMO) LTI systems with guaranteed parameter convergence. An online plant-parameter identification method is developed in conjunction with a direct control-parameter update law to ensure exponential convergence (after a tunable finite time) of tracking error as well as plant and control-parameter estimation errors to zero. Unlike the restrictive persistence of excitation (PE) condition required in classical MRAC approaches, this method guarantees parameter convergence by imposing a significantly milder initial excitation condition on the relevant signals. The introduction of a low-pass filter obviates the need for state derivative knowledge, whereas, the novel inclusion of an integral-like update in the plant-parameter estimation law overcomes the requirement of the restrictive PE condition. As far as the authors are aware, this is the first work on MRAC for MIMO linear time invariant (LTI) systems, which guarantees exponential convergence of the error dynamics without requiring the PE condition as well as the structural knowledge of the system matrices.

Parameter Identification of Linear Discrete-Time Systems with Guaranteed Transient Performance

Dynamic regressor extension and mixing is a new technique for parameter estimation that has proven instrumental in the solution of several open problems in system identification and adaptive control. A key property of the estimator is that, for linear regression models, it guarantees monotonicity of each element of the parameter error vector that is a much stronger property than monotonicity of the vector norm, as ensured with classical gradient or least-squares estimators. The main result of this paper is to give new techniques for deriving explicit conditions on the exogenously specified reference trajectory to guarantee parameter convergence for a class of linear discrete-time single-input single-output systems. A numerical example is given.

Adaptive Control of Delayed Teleoperation Systems with Parameter Convergence

It is well known that parameter convergence in adaptive control can bring about an improvement of system performance, including accurate online identification, exponential tracking, and robust adaptation without parameter drift. However, strong persistent-excitation (PE) or sufficient-excitement (SE) conditions should be satisfied to guarantee parameter convergence in the classical adaptive control. This paper proposes a novel adaptive control to guarantee parameter convergence without PE and SE conditions for nonlinear teleoperation systems with dynamic uncertainties and time-varying communication delays. The stability criterion of the closed-loop teleoperation system is given in terms of linear matrix inequalities. The effectiveness of this approach is illustrated by simulation studies, where both master and slave are assumed to be two-link manipulators with full nonlinear system dynamics.

Data-Driven Adaptive LQR for Completely Unknown LTI Systems

In this paper, a data-driven on-policy optimal control design is proposed for continuous-time linear time invariant (LTI) systems with completely unknown dynamics. An online system identifier and control gain parameter estimator, which use past and current data together with standard gradient descent update laws, facilitate the design of an adaptive optimal controller that guarantees parameter convergence without the need of persistence of excitation (PE). Unlike the classical approach of enforcing the restrictive PE condition on the regressor, the data-driven approach is verifiable online and establishes parameter convergence from information rich past stored data simultaneously with the current data. A state feedback controller is designed using a dynamic gain parameter which is shown to converge to the neighborhood of the optimal LQR gain. Semi-global uniformly ultimately bounded (UUB) stability of the overall system is established using Lyapunov-based analysis. Simulation results further validate the developed result.

Adaptive backstepping control for an engine cooling system with guaranteed parameter convergence under mismatched parameter uncertainties

This paper proposes a novel adaptive backstepping control for a special class of nonlinear systems with both matched and mismatched unknown parameters. The parameter update laws resemble a nonlinear reduced-order disturbance observer. Thus, the convergence of the estimated parameter values to the true ones is guaranteed. In each recursive design step, only single parameter update law is required in comparison to the existing standard adaptive backstepping techniques based on overparametrization and tuning functions. To make a fair comparison with the overparametrization and tuning function methods, a second-order nonlinear engine cooling system is taken as a benchmark problem. This system is subject to both matched and mismatched state-dependent lumped disturbances. Moreover, the proposed model-based controllers are compared with a classical PI control by using performance metrics, i.e., root-mean-square error and control effort. The comparative analysis based on these performance metrics, simulations as well as experiments highlights the effectiveness of the proposed novel adaptive backstepping control in terms of asymptotic tracking, global stability and guaranteed parameter convergence.

Model reference composite learning control without persistency of excitation

Parameter convergence is desirable in adaptive control as it brings several attractive features, including accurate online modelling, exponential tracking, and robust adaptation without parameter drift. However, a strong persistent-excitation (PE) condition must be satisfied to guarantee parameter convergence in the conventional adaptive control. This study proposes a model reference composite learning control strategy to guarantee parameter convergence without the PE condition. In the composite learning, an integral at a moving-time window is applied to construct a prediction error, an integral transformation is derived for avoiding the time derivation of plant states in the calculation of the prediction error, and both the tracking error and the prediction error are applied to update parametric estimates. Global exponential stability of the closed-loop system is established under an interval-excitation condition which is much weaker than the PE condition. Compared with a concurrent learning technique that has the same aim as this study, the proposed composite learning technique avoids the usage of singular value maximisation and fixed-point smoothing resulting in a considerable reduction of computational cost. Numerical results have verified effectiveness and superiority of the proposed control strategy.

Composite Learning From Adaptive Dynamic Surface Control

In the conventional adaptive control, a stringent condition named persistent excitation (PE) must be satisfied to guarantee parameter convergence. This technical note focuses on adaptive dynamic surface control for a class of strict-feedback nonlinear systems with parametric uncertainties, where a novel technique coined composite learning is developed to guarantee parameter convergence without the PE condition. In the composite learning, online recorded data together with instantaneous data are applied to generate prediction errors, and both tracking errors and prediction errors are utilized to update parametric estimates. The proposed approach is also extended to an output-feedback case by using a nonlinear separation principle. The distinctive feature of the composite learning is that parameter convergence can be guaranteed by an interval-excitation condition which is much weaker than the PE condition such that the control performance can be improved from practical asymptotic stability to practical exponential stability. An illustrative example is used for verifying effectiveness of the proposed approach.

Adaptive Sliding-Mode Control of an Innovative Engine Cooling System

Abstract: This paper proposes a novel adaptive sliding-mode control for an innovative engine cooling system under the influence of both matched and mismatched lumped disturbances. The parameter update laws resemble a nonlinear reduced-order disturbance observer and guarantee the convergence of the estimated parameter values to the real ones. Experiments on a dedicated test rig highlight the effectiveness of the proposed novel adaptive sliding-mode control in terms of asymptotic tracking, global stability and guaranteed parameter convergence. The closed-loop stability of the overall system is established by using Lyapunov’s direct method. To provide a fair comparison, the performance of the proposed controller is compared with a PI-controller.

Adaptive Multiple-Model Control of A Class of Nonlinear Systems

In this paper, an adaptive multiple-model controller is developed for nonlinear systems in parametric-strict-feedback form. Unlike the previous results, a switching scheme is not required here to switch the most appropriate model into the controller design. The new scheme reduces the number of identification models and uses information provided by all the models more efficiently than previous results by using the convex combination of estimates of parameters. The method guarantees parameter convergence and global asymptotic stability of the closed-loop system. The global boundness of closed-loop signals and asymptotic convergence to zero of tracking error are proved. A simulation example is included to demonstrate the effectiveness of the obtained results.

Mixed-Domain Adaptive Blind Correction of High-Resolution Time-Interleaved ADCs

Blind mismatch correction of time-interleaved analog-to-digital converters (TI-ADC) is a challenging task. We present a practical blind calibration technique for low-computation, low-complexity, and high-resolution applications. Its key features are: dramatically reduced computation; simple hardware; guaranteed parameter convergence with an arbitrary number of TI-ADC channels and most real-life input signals, with no bandwidth limitation; multiple Nyquist zone operation; and mixed-domain error correction. The proposed technique is experimentally verified by an 400 MSPS TI-ADC system. In a single-tone test, the proposed practical blind calibration technique suppressed mismatch spurs by 70 dB to 90 dB below the signal tone across the first two Nyquist zones (10 MHz to 390 MHz). A wideband signal test also confirms the proposed technique.

Parameter convergence in adaptive extremum-seeking control

This paper addresses the problem of parameter convergence in adaptive extremum-seeking control design. An alternate version of the popular persistence of excitation condition is proposed for a class of nonlinear systems with parametric uncertainties. The condition is translated to an asymptotic sufficient richness condition on the reference set-point. Since the desired optimal set-point is not known a priori in this type of problem, the proposed method includes a technique for generating perturbation signal that satisfies this condition in closed-loop. This demonstrates its superiority in terms of parameter convergence. The method guarantees parameter convergence with minimal but sufficient level of perturbation. The effectiveness of the proposed method is illustrated with a simulation example.