Decentralized Control of Nonlinear Large-Scale Systems Using Dynamic Output Feedback

In this paper, a kind of robust observer design scheme based on a constrained Lyapunov equation is presented for a class of non-linear interconnected systems using structural characteristics. The non-linear interconnected system is not required to be affine or linearizable. Both matched and unmatched uncertainties are considered, and a method to deal with uncertain interconnections is proposed. The bounding functions of all the uncertainties may be arbitrarily large since non-linear gain functions are introduced to eliminate the effects of the uncertainties by exploiting their structural characteristics. Simulation is given to demonstrate the effectiveness of the proposed scheme.

In this paper, asymptotic stabilization for a class of nonlinear large-scale systems with unmatched uncertainties is investigated. Two types of robust control algorithms are proposed to stabilize the uncertain nonlinear large-scale systems asymptotically provided that the nominal systems are asymptotically stable and the unmatched uncertainties are equivalently matched. The decentralized control utilizes the local state of each subsystems as the feedback information. The two-level control uses the local state as well as the states of the state of the connecting subsystems. An example is used to illustrate the proposed control method.

In this article, a novel high gain observer (HGO)-based decentralised indirect adaptive fuzzy controller is developed for a class of uncertain affine large-scale nonlinear systems. By the combination of fuzzy logic systems and an HGO, the state variables are not required to be measurable. The proposed feedback and adaptation mechanisms guarantee that each subsystem is able to adaptively compensate for interconnections and disturbances with unknown bounds. It is ascertained using a singular perturbation method that all the signals of the closed-loop large-scale system stand uniformly ultimately bounded and the tracking errors converge to tunable neighbourhoods of the origin. Simulation results of correlated double inverted pendulums substantiate the effectiveness of the proposed controller.

A novel decentralised indirect adaptive output feedback fuzzy controller with a compensation controller and an H ∞ tracking controller is presented for a class of uncertain large-scale nonlinear systems in this article. The compensator adaptively compensates for interconnections between subsystems as well as mismatched errors, while the H ∞ controller suppresses the effect of external disturbances. Based upon the combination of fuzzy inference systems, a state observer, H ∞ tracking technique and the strictly positive real condition, the proposed overall observer-based decentralised algorithm guarantees not only asymptotical tracking of reference trajectories but also an arbitrary small attenuation level of the unmodelled error dynamics including the disturbances on the tracking control. Simulation results substantiate the effectiveness of the proposed scheme.

The exact feedback linearization technique with partial state feedback and stable zero dynamics ensures local exponential stability. However, the method requires an accurate model, without uncertainties. The paper proposes an extension of the method for input-affine nonlinear systems with stable zero dynamics and matched uncertainties. Moreover, the weighted closed-loop sensitivity function is imposed using the ℒ<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf>-gain analysis. The advantage of the proposed extension is that it ensures both robust stability and performance (tailored to reference tracking) for the uncertain nonlinear system affected by the limitations of zero dynamics. The two methodologies are then illustrated on a given academic example.

In this paper, the problem of adaptive fuzzy decentralized optimal control is investigated for a class of nonlinear large-scale systems in strict-feedback form. The considered nonlinear large-scale systems contain the unknown nonlinear functions and unmeasured states. By utilizing the fuzzy logic systems to approximate the unknown nonlinear functions and cost functions, a fuzzy state observer is established to estimate the unmeasured states. The control design is divided into two phases. First, by using the state observer and the backstepping design technique, a feedforward decentralized controller with parameters adaptive laws is designed, by which the original controlled strict-feedback nonlinear large-scale system is transformed into an equivalent affine nonlinear large-scale system. Second, by using adaptive dynamic programming theory, a feedback decentralized optimal controller is developed for the equivalent affine nonlinear system. The whole adaptive fuzzy decentralized optimal control scheme consists of a feedforward decentralized controller and a feedback decentralized optimal controller. It is shown that the proposed adaptive fuzzy decentralized optimal control approach can guarantee that all the signals in the closed-loop system are bounded, and the tracking errors converge to a small neighborhood of zero. In addition, the proposed control approach can guarantee that the cost functions are minimized. Simulation results are given to demonstrate the effectiveness of the proposed control approach.

Employing predictive control strategy, a novel discrete-time variable structure control (VSC) algorithm is presented for a class of nonlinear uncertain systems. By applying reaching law and higher order sliding mode approaches, a creative higher order sliding mode prediction model (HOSMPM) is constructed, such that the future information of sliding mode can be used. Based on the HOSMPM and feedback correction, control law is obtained by virtue of receding horizon optimization. The robustness analysis proofs that the closed-loop systems possess strong robustness to matched or unmatched uncertainties, in the case of unknown boundaries of uncertainties. The validity of proposed VSC method is illustrated by a numerical simulation.

In this paper, we consider nested sliding mode control of SISO nonlinear systems to track a reference signal. The proposed system is perturbed by bounded matched and unmatched uncertainties and assumed to be in strict-feedback form. A step wise procedure is introduced to obtain the controller. In each step, a continuous sliding mode controller is designed as virtual control law. Then the next step sliding surface is defined by using this virtual controller. These sliding surfaces are selected as nonlinear static functions of the system states. Finally in the last step, smooth static state feedback control law is determined such that the output tracks the desired exogenous system output, while the system states are forced arbitrary close to the intersection of sliding surfaces and remain bounded.

A novel tracking control algorithm based on sliding mode prediction is proposed for a class of discrete-time nonlinear uncertain systems in this paper. By constructing a sliding mode prediction model at first, the future, present and history information of the system can be used to improve the performance of sliding mode control. Because of sliding mode reference trajectory, the reachability of sliding mode is achieved, and the reaching mode can be determined by designers in advance. Due to feedback correction and receding horizon optimization, the influence of uncertainty can be compensated in time and control law is obtained subsequently. Theoretical analysis proves the closed-loop system possesses robustness to matched or unmatched uncertainty, without requiring the known bound of uncertainty. Simulation results illustrate the validity of the presented algorithm.

This paper presents a solution to a robust optimal regulation problem for a nonlinear polynomial system affected by parametric and matched uncertainties, which is based only on partial state information. The parameters describing the dynamics of the nonlinear polynomial plant depend on a vector of unknown parameters, which belongs to a finite parametric set, and the application of a certain control input is associated with the worst or least favorable value of the unknown parameter. A high-order sliding mode state reconstructor is designed for the nonlinear plant in such a way that the previously designed control can be applied for a system with incomplete information. Additionally, the matched uncertainty is also compensated by means of the same output-based regulator. The obtained algorithm is applied to control a mechanical pendulum of the third order, successfully verifying the effectiveness of the developed approach.

This paper presents a decentralized adaptive controller for a class of large-scale nonlinear systems with unknown subsystems and interactions. A direct adaptive controller is devised based on Lyapunov stability analysis so that the stability of the closed loop system is guaranteed by introducing a suitably driven adaptive rule. The adaptive controller proposed in this paper can guarantee the stability of the closed-loop system without knowing the sign of the controller coefficient. To show the effectiveness of the proposed decentralized adaptive controller, a nonlinear system is chosen as a case study. Simulation results are very promising.

ABSTRACTThis work addresses the dynamic anti-windup design problem for a class of nonlinear systems subject to actuator saturation. The considered class regards the systems that can be cast in a differential algebraic representation (DAR), such as rational and polynomial systems. Considering that a nonlinear dynamic output feedback controller, which can also be written as a DAR, has been designed to stabilise the nonlinear system disregarding the saturation effects, LMI-based conditions are proposed to compute a stabilising dynamic anti-windup compensator. Two problems are considered: the first one regards the regional internal stabilisation; and the second one, assuming that an energy-bounded disturbance acts on the system, concerns the input-to-state stability. The derived conditions can therefore be incorporated in convex optimisation problems that allow to compute the anti-windup compensator in order to maximise the region of guaranteed asymptotic stability, to maximise a bound on the admissible -norm of the disturbance or even to minimise a bound on the -gain between the disturbance and the output. Numerical examples illustrate the proposed methods.

This paper presents a fuzzy basis function approach for adaptive decentralized control of a class of large-scale nonlinear systems with MIMO subsystems. Hybrid adaptive-robust tracking control schemes which are based on a combination of the H? tracking theory, and fuzzy control design are developed such that all the states and signals are bounded and the H? tracking control performance is guaranteed. In addition, each subsystem is able to adaptively compensate for disturbances and interconnections with unknown bounds. The resultant decentralized control with multi-controller architecture guarantee stability and convergence of the output errors to zero asymptotically, by local output-feedback. Simulation results on the control of a model of a nonlinear electrical machine are presented to illustrate the effectiveness of the proposed controller.

This technical note deals with asymptotic stabilization of general nonlinear discrete-time systems by dynamic output feedback control. First, a sufficient condition for the dynamic output feedback stabilization with the closed-loop domain of attraction (DOA) estimation is given. For a given Lyapunov function of the plant state and the controller state, the negative-definite domain (NDD) in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(z_+$</tex-math></inline-formula>-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$u$</tex-math></inline-formula>-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$z$</tex-math></inline-formula>-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$y)$</tex-math></inline-formula>-space is proposed, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$z_+,u,z$</tex-math></inline-formula>, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$y$</tex-math></inline-formula> denote the next controller state, the current control input, the current controller state and the current plant output, respectively. All points <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(z_+;u;z;y)$</tex-math></inline-formula> in the NDD can make the time difference of the Lyapunov function negative-definite for the controller state <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$z$</tex-math></inline-formula> and all plant states in a set of plant states, which is determined by the controller state <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$z$</tex-math></inline-formula> and the plant output <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$y$</tex-math></inline-formula>. The NDD in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(z_+$</tex-math></inline-formula>-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$u$</tex-math></inline-formula>-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$z$</tex-math></inline-formula>-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$y)$</tex-math></inline-formula>-space could be viewed as an unstructured dynamic output feedback stabilization controller set. And any invariant subset of the projection of the NDD in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(z_+$</tex-math></inline-formula>-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$u$</tex-math></inline-formula>-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$z$</tex-math></inline-formula>-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$y)$</tex-math></inline-formula>-space onto the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(z$</tex-math></inline-formula>-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$x)$</tex-math></inline-formula>-space is an estimate of the DOA for the closed-loop, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$x$</tex-math></inline-formula> denotes the current plant state. Second, based on the NDD, the controller design problem is converted to a set approximation problem in Euclidean space. Using numerical set approximation methods, dealing with strong nonlinearities is no longer the bottleneck. An estimation method for the unstructured dynamic output feedback stabilization controller set is proposed based on interval analysis, which is a kind of guaranteed numerical method for approximating sets.

Self-tuned local feedback gain based decentralized fault tolerant control for a class of large-scale nonlinear systems