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In this paper, the problem of local output regulation is considered. The presented results answer the question: given a controller solving the local output regulation problem, how to estimate the set of admissible initial conditions for which this controller makes the regulated output converge to zero. Theoretical estimation results and an estimation procedure explaining the application of these results...
In this paper, a new adaptive PID-type iterative learning controller (ILC) is proposed for a class of repeatable nonlinear systems with unknown nonlinearities. The initial state errors are allowed to be nonzero and varying for each iteration. The main structure of the adaptive PID-type ILC is constructed based on a time-varying boundary layer which is designed to overcome the problem of initial state...
Recent methods for gain scheduling controller design based on linear parameter-varying (LPV) systems offer a systematic way to obtain a nonlinear controller that covers different operating conditions. However, despite that the LPV synthesis part of the process of obtaining a gain scheduled controller is theoretically straight forward, the nonlinear closed loop system may be unstable for some operating...
It is an important question whether nonlinear controller design is needed for a particular application or whether linear controllers are sufficient to achieve the desired control goals. The present paper introduces the closed-loop optimal control law (OCL) nonlinearity measure, a new tool that provides a scheme to quantify the degree of nonlinearity of an optimal state feedback controller for a given...
An switching adaptive control scheme is presented, which provides global asymptotic stability property with respect to state space vector of the plant. In the presence of disturbance these schemes ensure boundedness of all trajectories of the system.
Contraction theory is a recent tool enabling to study the stability of nonlinear systems trajectories with respect to one another, and therefore belongs to the class of incremental stability methods. In this paper, we extend the original definition of contraction theory to incorporate in an explicit manner the control input of the considered system. Such an extension, called universal contraction,...
The problem of existence of continuous storage function for dissipative nonlinear systems is considered. It is shown that, if a nonlinear system is dissipative in the state x∗, then, under certain assumptions, a continuous storage function can be constructed on a set of points accessible from x∗ by concatenation of a finite number of forward and backward motions of the system. Most of these assumptions...
We present new characterizations of integral Input-Output-to-State Stability. This is a notion of dectectability formulated in the Input-to-State Stability framework. Equivalent properties are discussed in terms Lyapunov dissipation inequalities and asymptotic estimates of the state variables on the basis of external information provided by input and output signals.
A novel technique for synthesizing dynamic state feedback controllers that achieve practical input to state stability (PISS) property for nonlinear discrete-time systems is presented. The PISS controller design for the original system is solved via an auxiliary l∞-bounded (LIB) robustness synthesis problem for an auxiliary system. A complete solution for the LIB synthesis problem has been presented...
Synthesis of static anti-windup compensators is considered. LMI conditions are established for stability and performance analysis of the closed loop system. The performance criterion describes the servo problem for the resulting closed-loop piece-wise linear system. The synthesis of the anti-windup compensators will be given by some bilinear matrix inequalities.
In this paper, observer-based indirect adaptive fuzzy controller with sliding mode observer is proposed for a class of uncertain nonlinear systems. Using fuzzy logic systems to approximate the unknown nonlinear functions, which are constructed by the state variables, if they are not available, a sliding mode observer is used to estimate the state. Thus, a combination between an adaptive fuzzy control...
In this work a fixed one step ahead predictive control has been applied to control angular position and linear velocity of an electrical wheelchair. The purpose of such as controller is to assist wheelchair users providing an easier and safer navigation. In addition the importance of this type of control is its effect by operation of the feedforward path to follow in the future, on the other hand,...
For single-input single-output uncertain nonlinear system, we show how the problem of global robust stabilization via recursive design can be solved by using less conservative bounding functions. The system is assumed to have a gain bounded unknown nonlinear function with semi-strict feedback structure. Moreover we extend the obtained controller to have disturbance attenuation property by modifying...
This paper presents a hybrid variable structure control scheme for nonlinear systems. A hard variable structure control is constructed firstly for achieving uniform ultimate boundedness control. Then, a soft variable structure control using fuzzy logic is incorporated to help improve dynamic responses when trajectories enter into the ultimate bound. For practical consideration, we added a GA-based...
This paper addresses the problem of state reduction of nonlinear continuous-time systems. A novel method that relates to balanced truncation is presented and applied to examples. The method is computationally efficient and is applicable to relatively large systems.
The concept of algebraic reachability refers to the property of a system that every state from a sufficiently big subset of a state-space can be reached from a given inital state by applying an admissible input to the system. In this paper we study algebraic reachability of rational systems. We provide necessary and sufficient conditions for a rational system to be algebraically reachable (from an...
The problem of input-to-output stability for switched nonlinear systems is considered. Two approaches for switching between non-exponentially stable systems are proposed guaranteeing input-to-output stability for the switched system.
In this note we extend the design tool presented in [6] for robust stabilization of nonminimum-phase nonlinear systems to the case of output regulation problems. As in [6] we take advantage from a design tool known in the linear literature as “vibrational feedback” to handle the presence of unstable zero dynamics in output regulation problems in presence of uncertainties. This work frames in a research...
A well-known drawback of classical gain-scheduling methods is that they provide controllers which require to be checked after their synthesis: the immersion of a nonlinear system into a family of linear systems to build local control laws provides a global control law only effective on neighbourhoods. The aim of this paper is to expose a general algorithm able to provide a global control law which...
Many nonlinear systems are influenced by undesired external system inputs called disturbances. If such systems cannot be decoupled from the disturbances, it is necessary to compute a control law that reduces the influence of the disturbances with respect to the system outputs. The nonlinear disturbance rejecting controller is based on fundamental linear differential equations for the tracking error...
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