Hyungbo Shim

Brief Nonlinear observer design via passivation of error dynamics

We present a new design scheme of nonlinear state observers (global, full order, asymptotic observers) through passivation of the error dynamics. In order to consider passivity of the error dynamics for the observer problem, we place a conceptual input and output on the generalized error dynamics which also includes the plant, and the strictness of passivity is extended with respect to a set in which the estimation error becomes zero. Then, output feedback passivation for the error dynamics will lead to the construction of a state observer. It is also shown that a nonlinear observer is generally vulnerable to measurement disturbance, in the sense that even an arbitrarily small measurement disturbance can lead to a blowup of the error state. However, due to the passivity of the error dynamics, the proposed nonlinear injection gain can be easily modified for the observer to be robust to measurement disturbances.

Asymptotic controllability and observability imply semiglobal practical asymptotic stabilizability by sampled-data output feedback

It is shown, for general nonlinear systems, that asymptotic controllability and observability are sufficient for semiglobal practical asymptotic stabilization by output feedback. Indeed, as previously shown in the literature, asymptotic controllability implies the existence of a (discontinuous in general) state feedback that, when implemented by sample and hold, is semiglobally practically stabilizing and robust to measurement disturbance; moreover, a weak form of observability allows reconstruction of the state with arbitrary precision in an arbitrarily short amount of time. So, we can build an output feedback that operates periodically in two modes: an initial, small fraction of a sampling period is used to estimate the state, and the remainder of the sampling period is used to implement the state feedback control using the state estimate. Our stabilization results are presented not only for compact target sets (e.g., the origin) but also for noncompact target sets.

An Inner-Loop Controller Guaranteeing Robust Transient Performance for Uncertain MIMO Nonlinear Systems

An output-feedback controller has been recently proposed that has the following features: 1) it is an inner-loop controller so that it can be added on the existing closed-loop system working in harmony with a pre-designed (possibly non-robust) outer-loop controller; 2) it robustifies the closed-loop system in a way that the uncertain plant under external disturbance behaves like a disturbance-free nominal plant; and 3) it recovers the trajectory of the nominal closed-loop system in time domain. However, it is restricted to the single-input-single-output nonlinear systems. In this technical note, we extend this result for a class of multi-input-multi-output (MIMO) nonlinear systems having the same number of inputs and outputs. The tools used in this synthesis are the singular perturbation theory and the multi-variable circle criterion. An example shows the effectiveness of the proposed method.

Further results on robustness of (possibly discontinuous) sample and hold feedback

We demonstrate that sample and hold state feedback control (possibly discontinuous with respect to the state) is robust when the closed loop system possesses an appropriate Lyapunov function. We first show that if a Lyapunov decrease over sampling periods exists for the nominal system, this decrease can be maintained with some degradation relative to a sufficiently small additive perturbation. We then proceed to catalog several applications of this robustness, e.g., robustness to measurement noise, computational delays, or fast actuator dynamics.

Recursive nonlinear observer design: beyond the uniform observability

We propose a recursive design scheme of a state observer for multiple-input-multiple-output, partly lower triangular nonlinear systems. The design begins from the subdynamics far from the output and propagates to the subdynamics close to the output, recalling the backstepping scheme for nonlinear control. The proposed class of systems is fairly general since it includes nonuniformly observable and/or detectable multioutput systems. Error convergence to zero is proved assuming boundedness of inputs a posteriori (i.e., after the design), which is preferable whereas most results in the literature assume the boundedness; a priori (i.e., before the design). A global observer is proposed with the global Lipschitz condition of the system, but without any restriction on the size of Lipschitz coefficient. The Lipschitz condition can be removed when a semiglobal observer is of interest.

Set-point Control of Elastic Joint Robots Using only Position Measurements

Motivated by the dynamic output feedback passification results, point-to-point control laws for an elastic joint robot are presented when only the position measurements are available. The proposed method makes a parallel connection of the robot system and an input-dimensional linear system which obtains the effect of the desired differentiators. It is shown that the closed-loop nonlinear robot system can be rendered output strictly passive and the regulation of the system is achieved in the end. Robustness analysis is also given with regard to uncertainties on the robot parameters. Performance of the proposed control law is illustrated in the simulation studies of a manipulator with three revolute elastic joints.

Robust Adaptive Control for a Class of Nonlinear Systems with Complex Uncertainties

This paper considers a robust adaptive stabilization problem for a class of uncertain nonlinear systems which include an unknown virtual control coefficient, an unknown constant parameter, and a time-varying disturbance whose bound is unknown. We propose a new estimator for an unknown virtual control coefficient and present a robust adaptive backstepping design procedure which results in a smooth state feedback control law, a new two-dimensional parameter update law, and a C¹ Lyapunov function which is positive definite and proper.

Output feedback passification for nonlinear systems

In this paper, the problem of output feedback passification for nonlinear systems is considered. Contrary to the conventional methodologies, our approach does not require the normal form representation of the system. Motivated by two examples, which become passive by output feedback but do not have the normal form, we present a new necessary and sufficient condition for the problem. Comparison with the recent result also shows the generality of the proposed condition.In this paper basic concepts on the passivity, i. e. passivity, state feedback passivity and output feedback passivity, are reviewed. We propose sufficient conditions on static and dynamic output feedback passification. For static output feedback passification, the class of output feedback passive systems is extended with the help of a slightly modified storage function. Dynamic output feedback passification is achieved via observer based control and a supplementary input. Finally, asymptotic stabilization for a weak passive system is treated.

Robustness of discontinuous feedback via sample and hold control

We demonstrate that discontinuous feedback, either derived from or possessing a Lyapunov-type framework, can achieve robust stabilization to an attractor /spl Ascr/ by utilizing a sample and hold controller. Our results rely on one main theorem, which essentially states that if a Lyapunov decrease over sampling periods exists for the nominal system, this decrease can be maintained with some degradation relative to a sufficiently small additive perturbation. We then proceed to catalogue several applications of this robustness; e.g., robustness to measurement noise, computational delays, or fast actuator dynamics.

Formation Control Algorithm for Coupled Unicycle-Type Mobile Robots Through Switching Interconnection Topology

In this study, we address the formation control problem of coupled unicycle-type mobile robots, each of which can interact with its neighboring robots by communicating their position outputs. Each communication link between two mobile robots is assumed to be established according to the given time-varying interconnection topology that switches within a finite set of connected fixed undirected networks and has a non-vanishing dwell time. Under this setup, we propose a distributed formation control algorithm by using the dynamics extension and feedback linearization methods, and by employing a consensus algorithm for linear multi-agent systems which provides arbitrary fast convergence rate to the agreement of the multi-agent system. Finally, the proposed result is demonstrated through a computer simulation.