Showing papers in "International Journal of Robust and Nonlinear Control in 2008"

An online active set strategy to overcome the limitations of explicit MPC

Abstract: Nearly all algorithms for linear model predictive control (MPC) either rely on the solution of convex quadratic programs (QPs) in real time, or on an explicit precalculation of this solution for all possible problem instances. In this paper, we present an online active set strategy for the fast solution of parametric QPs arising in MPC. This strategy exploits solution information of the previous QP under the assumption that the active set does not change much from one QP to the next. Furthermore, we present a modification where the CPU time is limited in order to make it suitable for strict real-time applications. Its performance is demonstrated with a challenging test example comprising 240 variables and 1191 inequalities, which depends on 57 parameters and is prohibitive for explicit MPC approaches. In this example, our strategy allows CPU times of well below 100 ms per QP and was about one order of magnitude faster than a standard active set QP solver. Copyright © 2007 John Wiley & Sons, Ltd.

Higher order sliding modes

Abstract: One of the most important control problems is control under heavy uncertainty conditions. While there are a number of sophisticated methods like adaptation based on identification and observation, or absolute stability methods, the most obvious way to withstand the uncertainty is to keep some constraints by "brutal force". Indeed any strictly kept equality removes one " uncertainty dimension". The most simple way to keep a constraint is to react immediately to any deviation of the system stirring it back to the constraint by a sufficiently energetic effort. Implemented directly, the approach leads to so-called sliding modes, which become main operation modes in the variable structure systems (VSS) [55]. Having proved their high accuracy and robustness with respect to various internal and external disturbances, they also reveal their main drawback: the so-called chattering effect, i.e., dangerous high-frequency vibrations of the controlled system. Such an effect was considered as an obvious intrinsic feature of the very idea of immediate powerful reaction to the minutest deviation from the chosen constraint. Another important feature is proportionality of the maximal deviation from the constraint to the time interval between the measurements (or to the switching delay).

Higher‐order sliding‐mode observer for state estimation and input reconstruction in nonlinear systems

Abstract: In this paper, a higher-order sliding-mode observer is proposed to estimate exactly the observable states and asymptotically the unobservable ones in multi-input–multi-output nonlinear systems with unknown inputs and stable internal dynamics. In addition the unknown inputs can be identified asymptotically. Numerical examples illustrate the efficacy of the proposed observer. Copyright © 2007 John Wiley & Sons, Ltd.

High-order sliding-mode observer for a quadrotor UAV

Abstract: In this paper, a feedback linearization-based controller with a high-order sliding mode observer running parallel is applied to a quadrotor unmanned aerial vehicle. The high-order sliding mode observer works as an observer and estimator of the effect of the external disturbances such as wind and noise. The whole observer–estimator–control law constitutes an original approach to the vehicle regulation with minimal number of sensors. Performance issues of the controller–observer are illustrated in a simulation study that takes into account parameter uncertainties and external disturbances. Copyright © 2007 John Wiley & Sons, Ltd.

Linear Time Varying Model Predictive Control and its Application to Active Steering Systems: Stability Analysis and Experimental Validation

Abstract: A Model Predictive Control (MPC) approach for controlling an Active Front Steering (AFS) system in an autonomous vehicle is presented. At each time step a trajectory is assumed to be known over a finite horizon, and an MPC controller computes the front steering angle in order to best follow the desired trajectory on slippery roads at the highest possible entry speed. We start from the results presented in [2], [6] and formulate the MPC problem based on successive on-line linearization of the nonlinear vehicle model (LTV MPC). We present a sufficient stability conditions for such LTV MPC scheme. The condition is derived for a general class of nonlinear discrete time systems and results into an additional convex constraint to be included in the LTV MPC design. For the AFS control problem, we compare the proposed LTV MPC scheme against the LTV MPC scheme in [6] where stability has been enforced with an ad-hoc constraint. Simulation and experimental tests up to 21 m/s on icy roads show the effectiveness of the LTV MPC formulation.

Exponential H∞ filtering for uncertain discrete‐time switched linear systems with average dwell time: A µ‐dependent approach

Abstract: In this paper, the problem of exponential H∞ filter problem for a class of discrete-time polytopic uncertain switched linear systems with average dwell time switching is investigated. The exponential stability result of the general discrete-time switched systems using a discontinuous piecewise Lyapunov function approach is first explored. Then, a new µ-dependent approach is proposed, which means the analysis or synthesis of the underlying systems is dependent on the increase degree µ of the piecewise Lyapunov function at the switching instants. A mode-dependent full-order filter is designed such that the developed filter error system is robustly exponentially stable and achieves an exponential H∞ performance. Sufficient existence conditions for the desired filter are derived and formulated in terms of a set of linear matrix inequalities, and consequently the minimal average dwell time and the corresponding filter are obtained from such conditions for a given system decay degree. A numerical example is presented to demonstrate the potential and effectiveness of the developed theoretical results.

State feedback controller design of networked control systems with interval time-varying delay and nonlinearity

Abstract: SUMMARY This paper proposes a method for robust state feedback controller design of networked control systems with interval time-varying delay and nonlinearity. The key steps in the method are to construct an improved interval-delay-dependent Lyapunov functional and to introduce an extended Jessen’s inequality. Neither free weighting nor model transformation are employed in the derivation of the system stability criteria. It is shown that the maximum allowable bound on the nonlinearity could be computed through solving a constrained convex optimization problem; and the maximum allowable delay bound and the feedback gain of a memoryless controller could be derived by solving a set of linear matrix inequalities (LMIs). Numerical examples are given to demonstrate the efiectiveness of the proposed method.

Blood glucose regulation using higher‐order sliding mode control

Abstract: Diabetes is discussed as a serious condition in which the body's production and use of insulin are impaired, causing glucose concentration level to increase in the bloodstream. In this paper, higher-order sliding mode control techniques, in specific prescribed convergence law, quasi-continuous and super-twisting control algorithms, are used to robustly stabilize the glucose concentration level of a diabetic patient in presence of the parameter variations and meal disturbance. The structure of the proposed higher-order sliding mode controllers is appropriate for making the insulin delivery pumps in closed-loop control of diabetes. A computer simulation is performed to manifest the theoretical analysis. The super-twisting algorithm is employed to attenuate the effect of chattering and obtain continuous control in the simulations. The efficiency of the proposed controller, i.e. robustness and high accuracy, in presence of physical disturbances like food intake and parametric uncertainties is verified via simulations. Copyright © 2007 John Wiley & Sons, Ltd.

An improved characterization of bounded realness for singular delay systems and its applications

Abstract: This paper is concerned with establishing a delay-dependent bounded real lemma (BRL) for singular systems with a time delay. Without resorting to any bounding techniques for some cross terms and model transformation, a new version of BRL for such systems is proposed, which guarantees a singular system to be regular, impulse free and stable while satisfying a prescribed H∞ performance level for any delays smaller than a given upper bound. Based on this, an H∞ state feedback controller is designed via a linear matrix inequality approach. The BRL, stability as well as H∞ results developed in this paper are less conservative than existing ones in the literature, which is demonstrated by providing some numerical examples. Copyright © 2007 John Wiley & Sons, Ltd.

Shortest path stochastic control for hybrid electric vehicles

Abstract: When a hybrid electric vehicle (HEV) is certified for emissions and fuel economy, its power management system must be charge sustaining over the drive cycle, meaning that the battery state of charge (SOC) must be at least as high at the end of the test as it was at the beginning of the test. During the test cycle, the power management system is free to vary the battery SOC so as to minimize a weighted combination of fuel consumption and exhaust emissions. This paper argues that shortest path stochastic dynamic programming (SP-SDP) offers a more natural formulation of the optimal control problem associated with the design of the power management system because it allows deviations of battery SOC from a desired setpoint to be penalized only at key off. This method is illustrated on a parallel hybrid electric truck model that had previously been analyzed using infinite-horizon stochastic dynamic programming with discounted future cost. Both formulations of the optimization problem yield a time-invariant causal state-feedback controller that can be directly implemented on the vehicle. The advantages of the shortest path formulation include that a single tuning parameter is needed to trade off fuel economy and emissions versus battery SOC deviation, as compared with two parameters in the discounted, infinite-horizon case, and for the same level of complexity as a discounted future-cost controller, the shortest-path controller demonstrates better fuel and emission minimization while also achieving better SOC control when the vehicle is turned off. Linear programming is used to solve both stochastic dynamic programs. Copyright © 2007 John Wiley & Sons, Ltd.

Output-feedback control of a class of stochastic nonlinear systems with linearly bounded unmeasurable states

Abstract: SUMMARY In this paper, the problems of stochastic disturbance attenuation and asymptotic stabilization via output feedback are investigated for a class of stochastic nonlinear systems with linearly bounded unmeasurable states. For the first problem, under the condition that the stochastic inverse dynamics are generalized stochastic input-to-state stable, a linear output-feedback controller is explicitly constructed to make the closed-loop system noise-to-state stable. For the second problem, under the conditions that the stochastic inverse dynamics are stochastic input-to-state stable and the intensity of noise is known to be a unit matrix, a linear output-feedback controller is explicitly constructed to make the closed-loop system globally asymptotically stable in probability. Using a feedback domination design method, we construct these two controllers in a unified way. Copyright # 2007 John Wiley & Sons, Ltd. Received 1 January 2007; Revised 29 April 2007; Accepted 7 June 2007

A new algorithm for high-order sliding mode control

Abstract: A new robust high-order sliding mode controller for a class of uncertain minimum-phase single-input–single-output (SISO) nonlinear systems is designed. The high-order sliding mode problem is formulated in input–output term and is viewed in uncertain linear context by considering uncertain nonlinear functions as bounded non-structured parametric uncertainties. A sliding manifold is designed in order to ensure finite-time convergence of sliding variable and its high-order time derivatives. The control law allows the establishment of an rth-order sliding mode. This result is extended to multi-input–multi-output (MIMO) systems. Copyright © 2007 John Wiley & Sons, Ltd.

Second-order sliding mode control of underactuated mechanical systems I: Local stabilization with application to an inverted pendulum

Abstract: Second order sliding mode control synthesis is developed for underactuated mechanical systems, operating under uncertainty conditions. In order to locally stabilize an underactuated system around an unstable equilibrium, an output is specified in such a way that the corresponding zero dynamics is locally asymptotically stable. Then, the desired stability property of the closed-loop system is provided by applying a quasihomogeneous second order sliding mode controller, driving the system to the zero dynamics manifold in finite time. Although the present synthesis exhibits an infinite number of switches on a finite time interval, it does not rely on the generation of first order sliding modes, while providing robustness features similar to those possessed by their standard sliding mode counterparts. A second order sliding mode appears on the zero dynamics manifold which is of co-dimension greater than the control space dimension. Performance issues of the proposed synthesis are illustrated in numerical and experimental studies of a cart-Pendulum system.

ℒ︁2‐Gain analysis and control of uncertain nonlinear systems with bounded disturbance inputs

Abstract: This paper proposes a convex approach to regional stability and ℒ2-gain analysis and control synthesis for a class of nonlinear systems subject to bounded disturbance signals, where the system matrices are allowed to be rational functions of the state and uncertain parameters. To derive sufficient conditions for analysing input-to-output properties, we consider polynomial Lyapunov functions of the state and uncertain parameters (assumed to be bounded) and a differential-algebraic representation of the nonlinear system. The analysis conditions are written in terms of linear matrix inequalities determining a bound on the ℒ2-gain of the input-to-output operator for a class of (bounded) admissible disturbance signals. Through a suitable parametrization involving the Lyapunov and control matrices, we also propose a linear (full-order) output feedback controller with a guaranteed bound on the ℒ2-gain. Numerical examples are used to illustrate the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd.

Robust fault estimation of uncertain systems using an LMI‐based approach

Abstract: General recent techniques in fault detection and isolation (FDI) are based on H∞ optimization methods to address the issue of robustness in the presence of disturbances, uncertainties and modeling errors. Recently developed linear matrix inequality (LMI) optimization methods are currently used to design controllers and filters, which present several advantages over the Riccati equation-based design methods. This article presents an LMI formulation to design full-order and reduced-order robust H∞ FDI filters to estimate the faulty input signals in the presence of uncertainty and model errors. Several cases are examined for nominal and uncertain plants, which consider a weight function for the disturbance and a reference model for the faults. The FDI LMI synthesis conditions are obtained based on the bounded real lemma for the nominal case and on a sufficient extension for the uncertain case. The conditions for the existence of a feasible solution form a convex problem for the full-order filter, which may be solved via recently developed LMI optimization techniques. For the reduced-order FDI filter, the inequalities include a non-convex constraint, and an alternating projections method is presented to address this case. The examples presented in this paper compare the simulated results of a structural model for the nominal and uncertain cases and show that a degree of conservatism exists in the robust fault estimation; however, more reliable solutions are achieved than the nominal design. Copyright © 2008 John Wiley & Sons, Ltd.

Tree search algorithm for assigning cooperating UAVs to multiple tasks

Abstract: This paper describes a tree search algorithm for assigning cooperating homogeneous uninhabited aerial vehicles to multiple tasks. The combinatorial optimization problem is posed in the form of a decision tree, the structure of which enforces the required group coordination and precedence for cooperatively performing the multiple tasks. For path planning, a Dubin's car model is used so that the vehicles' constraint, of minimum turning radius, is taken into account. Due to the prohibitive computational complexity of the problem, exhaustive enumeration of all the assignments encoded in the tree is not feasible. The proposed optimization algorithm is initialized by a best-first search and candidate optimal solutions serve as a monotonically decreasing upper bound for the assignment cost. Euclidean distances are used for estimating the path length encoded in branches of the tree that have not yet been evaluated by the computationally intensive Dubin's optimization subroutine. This provides a lower bound for the cost of unevaluated assignments. We apply these upper and lower bounding procedures iteratively on active subsets within the feasible set, enabling efficient pruning of the solution tree. Using Monte Carlo simulations, the performance of the search algorithm is analyzed for two different cost functions and different limits on the vehicles' minimum turn radius. It is shown that the selection of the cost function and the limit have a considerable effect on the level of cooperation between the vehicles. The proposed deterministic search method can be applied on line to different sized problems. For small-sized problems, it provides the optimal solution. For large-sized problems, it provides an immediate feasible solution that improves over the algorithm's run time. When the proposed method is applied off line, it can be used to obtain the optimal solution, which can be used to evaluate the performance of other sub-optimal search methods. Copyright © 2007 John Wiley & Sons, Ltd.

On complete Lyapunov–Krasovskii functional techniques for uncertain systems with fast-varying delays

Abstract: Stability of linear systems with norm-bounded uncertainties and uncertain time-varying delays is considered. The delay is supposed to be bounded and fast varying (without any constraints on the delay derivative). Sufficient stability conditions are derived by direct Lyapunov method based on the complete Lyapunov-Krasovskii functional (LKF). A novel complete LKF construction is presented the derivative condition for the nominal LKF (i.e. for the LKF, which corresponds to the system with the nominal values of the coefficients and of the delay) depends on the 'present' state only. The comprehensive technique for stability analysis of uncertain time-delay systems is extended to the case of complete LKF the application of free weighting matrices (instead of descriptor model transformation) and of Jensen's inequality (instead of the cross-terms bounding). Numerical examples illustrate the efficiency of the method, and complete the paper. Copyright (c) 2007 John Wiley and Sons, Ltd.

Fast implementations and rigorous models: Can both be accommodated in NMPC?

Abstract: In less than two decades, nonlinear model predictive control has evolved from a conceptual framework to an attractive, general approach for the control of constrained nonlinear processes. These advances were realized both through better understanding of stability and robustness properties as well as improved algorithms for dynamic optimization. This study focuses on recent advances in optimization formulations and algorithms, particularly for the simultaneous collocation-based approach. Here, we contrast this approach with competing approaches for online application and discuss further advances to deal with applications of increasing size and complexity. To address these challenges, we adapt the real-time iteration concept, developed in the context of multiple shooting (Real-Time PDE-Constrained Optimization. SIAM: Philadelphia, PA, 2007; 25–52, 3–24), to a collocation-based approach with a full-space nonlinear programming solver. We show that straightforward sensitivity calculations from the Karush–Kuhn–Tucker system also lead to a real-time iteration strategy, with both direct and shifted variants. This approach is demonstrated on a large-scale polymer process, where online calculation effort is reduced by over two orders of magnitude. Copyright © 2007 John Wiley & Sons, Ltd.

Robust stabilization for uncertain discrete singular systems with state delay

Abstract: The robust stabilization problem for uncertain discrete singular time-delay systems is addressed in this paper. In terms of strict linear matrix inequality and a finite sum inequality, a delay-dependent criterion for the nominal systems to be admissible is obtained. Based on the criterion, a state feedback controller, which guarantees that, for all admissible uncertainties, the resulting closed-loop system is regular, causal and stable, is constructed. An explicit expression for the desired controller is also given. The obtained results include both delay-independent and delay-dependent cases. Some numerical examples are introduced to show the effectiveness of the given results. Copyright © 2008 John Wiley & Sons, Ltd.

A robust approach to the UAV task assignment problem

Abstract: This paper presents a new robust approach to the task assignment of unmanned aerial vehicles (UAVs) operating in uncertain dynamic environments for which the optimization data, such as target cost and target–UAV distances, are time varying and uncertain. The impact of this uncertainty in the data is mitigated by tightly integrating two approaches for improving the robustness of the assignment algorithm. One approach is to design task assignment plans that are robust to the uncertainty in the data, which reduces the sensitivity to errors in the situational awareness (SA), but can be overly conservative for long duration plans. A second approach is to replan as the SA is updated, which results in the best plan given the current information, but can lead to a churning type of instability if the updates are performed too rapidly. The strategy proposed in this paper combines robust planning with the techniques developed to eliminate churning. This combination results in the robust filter-embedded task assignment algorithm that uses both proactive techniques that hedge against the uncertainty, and reactive approaches that limit churning behavior by the vehicles. Numerous simulations are shown to demonstrate the performance benefits of this new algorithm. Copyright © 2007 John Wiley & Sons, Ltd.

Residual vibration suppression using Hankel iterative learning control

Abstract: In this paper, we present a new approach for suppression of residual vibrations in point-to-point motions based on lifted iterative learning control (ILC). The approach is to add a signal to the command input during the point-to-point motion in order to compensate for residual vibrations. A special form of ILC with separate actuation and observation time windows is shown to converge to the required signal. Subsequently, we present ILC control strategies for residual vibration suppression in which convergence and performance specifications can be designed separately. Additionally, the designed controllers have the capability to constrain the amplitude of the command signal. The presented strategies are demonstrated on a flexible system and shown to be successful in the suppression of residual vibration while minimizing the maximum amplitude of the command signal. Copyright © 2007 John Wiley & Sons, Ltd.

Actuator fault diagnosis for uncertain linear systems using a high‐order sliding‐mode robust differentiator (HOSMRD)

Abstract: Many observer-based fault diagnosis strategies proposed for linear systems, subject to unknown inputs, operate based on three assumptions. The first assumption is that the system under consideration is at least detectable. The second one is that the unknown inputs satisfy certain matching conditions. The third one, which is often implicit, is that the relative degrees from the generalized input vector, including both known and unknown inputs, to the outputs are no larger than one. If none of these assumptions are met, little result exists on how to carry out fault diagnosis. The purpose of this paper is to develop a novel actuator fault diagnosis scheme for a general class of linear systems subject to unknown inputs that can work without the mentioned three assumptions. Four actuator fault diagnosis problems related to fault detection, isolation, and estimation are formulated and studied. In order to solve these problems, an input–output relation, which involves only the outputs and their higher-order derivatives, is derived. The posed problems are solved based on this relation via utilizing both the outputs and their higher-order derivatives. Because only the outputs are measured, higher-order output derivatives are estimated using the recently developed high-order sliding-mode robust differentiators (HOSMRDs). The first two fault detection and isolation problems are answered in terms of a concept called Generalized Actuator Fault Isolation IndeX (GAFIX), and it is proved that, under the condition that the derived input–output relation is used for fault diagnosis, actuator faults are detectable if and only if GAFIX⩾1, and l actuator faults can be isolated if and only if GAFIX⩾l+1. A method which can be used to estimate the faults is proposed for the fault estimation problem. To solve the last problem, an actuator fault diagnosis scheme is designed using both the measured outputs and their estimated derivatives obtained by HOSMRDs, and is presented in steps. Finally, an example is provided to show the effectiveness of our fault diagnosis scheme in terms of fault detection, isolation, and estimation. Copyright © 2007 John Wiley & Sons, Ltd.

Input-to-state stabilizing sub-optimal NMPC with an application to DC–DC converters

Abstract: This article focuses on the synthesis of computationally friendly sub-optimal nonlinear model predictive control (NMPC) algorithms with guaranteed robust stability. To analyse the robustness of the MPC closed-loop system, we employ the input-to-state stability (ISS) framework. To design ISS sub-optimal NMPC schemes, a new Lyapunov-based method is proposed. ISS is ensured via a set of constraints, which can be specified as a finite number of linear inequalities for input affine nonlinear systems. Furthermore, the method allows for online optimization over the ISS gain of the resulting closed-loop system. The potential of the developed theory for the control of fast nonlinear systems, with sampling periods below 1 ms, is illustrated by applying it to control a Buck-Boost DC–DC converter. Copyright © 2007 John Wiley & Sons, Ltd.

Second‐order sliding mode control of underactuated mechanical systems II: Orbital stabilization of an inverted pendulum with application to swing up/balancing control

Abstract: Orbital stabilization of an underactuated cart-pendulum system is under study. The quasihomogeneous control synthesis is utilized to design a second order sliding mode controller that drives the actuated cart to a periodic reference orbit in finite time, while the non-actuated pendulum produces bounded oscillations. A modified Van der Pol oscillator is introduced into the synthesis as an asymptotic generator of the periodic motion. The resulting closed-loop system is capable of moving from one orbit to another by simply changing the parameters of the Van der Pol modification. Performance issues of the proposed synthesis are illustrated in numerical and experimental studies of the swing up/balancing control problem of moving a pendulum, located on an actuated cart, from its stable downward position to the unstable inverted position and stabilizing it about the vertical.

Delay‐range‐dependent robust stability and stabilization for uncertain systems with time‐varying delay

Abstract: This paper concerns delay-range-dependent robust stability and stabilization for time-delay system with linear fractional form uncertainty. The time delay is assumed to be a time-varying continuous function belonging to a given range. On the basis of a novel Lyapunov–Krasovskii functional, which includes the information of the range, delay-range-dependent stability criteria are established in terms of linear matrix inequality. It is shown that the new criteria can provide less conservative results than some existing ones. Moreover, the stability criteria are also used to design the stabilizing state-feedback controllers. Numerical examples are given to demonstrate the applicability of the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd.

Generalized homogeneous quasi‐continuous controllers

Abstract: A new class of arbitrary-order homogeneous quasi-continuous sliding-mode controllers containing numerous functional parameters is proposed. All the controllers also have robust output-feedback versions. A numerical procedure is established for the first time for setting the controller parameters. A finite-time stable 5-sliding mode is demonstrated for the first time. Copyright © 2007 John Wiley & Sons, Ltd.

A UD factorization‐based nonlinear adaptive set‐membership filter for ellipsoidal estimation

Abstract: The extended set-membership filter (ESMF) for nonlinear ellipsoidal estimation suffers from numerical instability, computation complexity as well as the difficulty in filter parameter selection. In this paper, a UD factorization-based adaptive set-membership filter is developed and applied to nonlinear joint estimation of both time-varying states and parameters. As a result of using the proposed UD factorization, combined with a new sequential and selective measurement update strategy, the numerical stability and real-time applicability of conventional ESMF are substantially improved. Furthermore, an adaptive selection scheme of the filter parameters is derived to reduce the computation complexity and achieve sub-optimal estimation. Simulation results have shown the efficiency and robustness of the proposed method. Copyright © 2007 John Wiley & Sons, Ltd.

Controllability and motion planning of a multibody Chaplygin's sphere and Chaplygin's Top

Abstract: SUMMARY This paper studies local configuration controllability of multibody systems with nonholonomic constraints. As a nontrivial example of the theory, we consider the dynamics and control of a multibody spherical robot. Internal rotors and sliders are used as the mechanisms for control. Our model is based on equations developed by the second author for certain mechanical systems with nonholonomic constraints, e.g. Chaplygin’s sphere and Chaplygin’s top in particular, and the multibody framework for unconstrained mechanical systems developed by the first and third authors. Recent methods for determining controllability and path planning for multibody systems with symmetry are extended to treat a class of mechanical systems with nonholonomic constraints. Specific results on the controllability and path planning of the spherical robot model are presented. Copyright q 2007 John Wiley & Sons, Ltd. Received 16 February 2007; Revised 23 May 2007; Accepted 23 June 2007

Robust adaptive output-feedback control for nonlinear systems with output unmodeled dynamics

Abstract: In this paper, for a class of uncertain nonlinear systems in the presence of inverse dynamics, output unmodeled dynamics and nonlinear uncertainties, a robust adaptive output-feedback controller design is proposed by combining small-gain theorem, changing supply function techniques with backstepping methods. It is shown that all the signals of the closed-loop system are uniformly bounded in biased case, and the output can be regulated to a small neighborhood of the origin in unbiased case. Furthermore, under some additional assumptions, an asymptotical result is obtained.