Small-gain Methods Research Articles

Continuous‐discrete high gain observer design with PI output predictor

SummaryIn this article, a continuous‐discrete high gain observer with a proportional integral (PI) output predictor structure is designed for a class of nonlinear systems subject to sampled‐delayed data measurements. To counteract the effect of the well‐known sensitivity of the high gain observer to the noise measurements, a novel PI output predictor structure is proposed. The uniform ultimate boundedness (UUB) of the proposed observer is demonstrated by means of Lyapunov function and small gain method. The effectiveness of our proposed observer is demonstrated through numerical simulations and performances comparison with previous observer design methods in the literature.

A Generalized Passivity-Based Stability Criterion for Assessing Large Signal Stability of Interconnected DC Power Systems

With the growing need to support large dynamic electric loads in microgrid environments, there has been a necessary push toward highly regulated dc distribution through power electronics. Unfortunately, these systems are nonlinear by nature and provide potentially destabilizing behavior at their source interfaces. To complicate matters further, many systems are built from independently designed subcomponents with little information shared between designs. It is, therefore, necessary to have stability-driven design requirements for each subsystem to enforce stable dynamics upon system integration. Traditional techniques are currently limited to either overly conservative large signal small-gain methods or small signal transfer function approaches that are unreliable for assuring large signal stability. This article proposes a generalized passivity-based stability criterion that conservatively estimates the domain of stability for an integrated nonlinear system. Through passivity partitioning and uniquely driven domain of passivity estimation techniques, this methodology provides interface conditions that certify stability while only requiring a reduced subset of knowledge of each connected subsystem <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">.</b>

Improved Robust Performance Design for Passive Uncertain Systems—Active Use of the Uncertainty Phase and Gain

In the robust performance design, the celebrated $\mu$ -synthesis provides a reputed tool for systems with norm-bounded uncertainty. However, such small-gain methods inevitably limit the achievable robust performance when the dynamic uncertainty is not characterized by its gain bound. To achieve a high robust performance for systems with positive real (PR) uncertainty, an output strict passivity (OSP) approach is proposed recently which makes use of the positive realness and the maximum gain information of the uncertainty. Aiming at an even higher robust performance, this article proposes a novel model for PR uncertainties which captures the frequency-dependent gain bound, and establishes the corresponding design theory to actively utilize both gain and phase bounds of the uncertainty in the robust performance design. A case study reveals that the new uncertainty model alone yields a substantial improvement over the OSP method in performance even under the same design setup. Moreover, the best tuned controller outperforms the OSP controller.

Adaptive Quantized Control of Output Feedback Nonlinear Systems With Input Unmodeled Dynamics Based on Backstepping and Small-Gain Method

In this article, an adaptive quantized neural backstepping strategy is investigated for a class of nonlinear systems with input unmodeled dynamics and output constraints based on the small-gain method. A challenge lies in the considered input-quantized actuator possessing both unknown control gain and input unmodeled dynamics, and the application of the small-gain theorem when the system possesses input unmodeled dynamics and the output constraints. By the coordinate transformation of the state variables, the input unmodeled dynamics subsystem is transformed into a suitable form for applying the small-gain theorem. By a logarithmic one to one mapping, the time-varying output constraints are tackled. With these methods, the stability proof based on the small-gain theorem is completed. It is shown that all the signals are bounded, and the output signal is constrained within the preset range.

Three-dimensional formation control based on nonlinear small gain method for multiple underactuated underwater vehicles

This paper proposes a distributed formation tracking controller for multiple underactuated underwater vehicles (UUVs) which move in three dimensional space. The formation controller designing process is divided into two parts. In the first part, the condition which the formation controller must be satisfied is given. And the controllers are designed to ensure the condition mentioned before. In the second part, decentralized formation controller are proposed, and the stability analysis based on small gain theorem is introduced. Simulation results illustrate that the designed controller can track three-dimensional formation trajectory accurately.

A small-gain method for integrated guidance and control in terminal phase of reentry

The guidance and control systems of reentry vehicles are usually designed separately and then integrated, but the scheme can be argued that synergistic relationships between the two subsystems are not fully exploited. In order to improve the performance of reusable launch vehicles (RLVs), this paper proposes an integrated guidance and control law for approach and landing of a RLV. According to the idea of reference-trajectory guidance, the angle of attack and bank angle commands are designed using sliding mode control (SMC) method to make the reference-trajectory tacking error converge into a small neighborhood of zero. An integrated guidance and control (IGC) law is developed utilizing generalized small-gain theorem to enforce the commands, and theoretical analysis shows that the law can guarantee the stability of the overall system. The Monte Carlo simulation confirms the effectiveness of the proposed design approach.

Event-based control of nonlinear systems with partial state and output feedback

This paper studies the event-triggered control problem for nonlinear systems with partial state and output feedback. We first consider the control systems that are transformable into an interconnection of two input-to-state stable (ISS) subsystems with the sampling error as the external input. It is shown that infinitely fast sampling can be avoided and asymptotic stabilization can be achieved by appropriately choosing the decreasing rate of the threshold signal of the event-trigger. Then, we focus on the event-triggered output-feedback control problem for nonlinear uncertain systems in the output-feedback form. The key idea is to introduce a novel nonlinear observer-based control design and to transform the control system into the form of interconnected ISS systems. ISS small-gain methods are used as a fundamental tool in the discussions.