Input-to-state Practically Stable Research Articles

Control of LPV Modeled AC-Microgrid Based on Mixed H2/H∞ Time-Varying Linear State Feedback and Robust Predictive Algorithm

This paper presents a robust model predictive control (RMPC) method with a new mixed H2/<inline-formula> <tex-math notation="LaTeX">$\text{H}\infty $ </tex-math></inline-formula> linear time-varying state feedback design. In addition, we propose a linear parameter-varying model for inverters in a microgrid (MG), in which disturbances and uncertainty are considered, where the inverters connect in parallel to renewable energy sources (RES). The proposed RMPC can use the gain-scheduled control law and satisfy both the H2 and <inline-formula> <tex-math notation="LaTeX">$\text{H}\infty $ </tex-math></inline-formula> proficiency requirements under various conditions, such as disturbance and load variation. A multistep control method is proposed to reduce the conservativeness caused by the unique feedback control law, enhance the control proficiency, and strengthen the RMPC feasible area. Furthermore, a practical and efficient RMPC is designed to reduce the online computational burden. The presented controller can implement load sharing among distributed generators (DGs) to stabilize the frequency and voltage of an entire smart island. The proposed strategy is implemented and studied in a MG with two DG types and various load types. Specifically, through converters, one type of DGs is used to control frequency and voltage, and the other type is used to control current. These two types of DGs operate in a parallel mode. Simulation results show that the proposed RMPCs are input-to-state practically stable (ISpS). Compared with other controllers in the literature, the proposed strategy can lead to minor total harmonic distortion (THD), lower steady-state error, and faster response to system disturbance and load variation.

Adaptive Neural Control for Switched Nonlinear Systems With Unstable Dynamic Uncertainties: A Small Gain-Based Approach.

This article concentrates on the adaptive neural control for switched nonlinear systems interconnected with unmodeled dynamics. The investigated model consists of two dynamic processes, namely, the x -system and the unmodeled z -dynamics. In this article, we focus on a scenario that the unmodeled z -dynamics do not contain input-to-state practically stable (ISpS) modes, that is, all modes are not ISpS (non-ISpS). First, we design an adaptive neural controller such that each mode of the closed-loop x -system is ISpS with respect to the state of dynamic uncertainties. Then, fast average dwell time (fast ADT) and slow average dwell time (slow ADT) are simultaneously used to limit the switching law. In this way, both the closed-loop x -system and the unmodeled z -dynamics are ISpS under switching. By assigning the ISpS gains with small-gain theorem, we can guarantee that the whole closed-loop system is semiglobal uniformly ultimately bounded (SGUUB), and meanwhile, the system output is steered to a small region of zero. Finally, simulation examples are used to verify the effectiveness of the proposed control scheme.

Adaptive fuzzy tracking control for nonlinear strict-feedback systems with unmodeled dynamics via backstepping technique

This paper considers an output tracking control problem with unmodeled dynamics for a class of nonlinear strict-feedback systems, which possess unstructured uncertainties and dynamic disturbances. Uncertain nonlinearities contain both unmeasured states and measurable output. A direct tracking controller is obtained on the basic of the backstepping and fuzzy logic system. By the use of small-gain approach, the discussed closed-loop system is proved to be input-to-state practically stable (ISpS) and all the parameter signals are semi-globally uniformly ultimately bounded. There are three adaptive parameters in the fuzzy controller. Finally, simulation examples are given to illustrate the efficiency of the proposed approach.

Distributed Nonlinear MPC of Multi-Agent Systems With Data Compression and Random Delays

This note proposes an Input to State practically Stable (ISpS) formulation of distributed nonlinear model predictive controller (NMPC) for formation control of constrained autonomous vehicles in presence of communication bandwidth limitation and transmission delays. Planned trajectories are compressed using neural networks resulting in considerable reduction of data packet size, while being robust to propagation delays and uncertainty in neighbors' trajectories. Collision avoidance is achieved by means of spatially filtered potential field. Analytical results proving ISpS and generalized small gain conditions are presented for both strongly-and weakly-connected networks, and illustrated by simulations.

ISPS-modular command-filtered adaptive back-stepping control of non-linearly parameterized pure-feedback systems

An input-to-state practically stable (ISPS)-modular command-filtered adaptive back-stepping control (CFABC) is investigated for non-linearly parameterized pure-feedback systems, which can obviate the complicate analytic derivatives in traditional back-stepping design. In the proposed CFABC scheme, sliding-mode-based integral filters are introduced to approximate the virtual control derivatives, to solve the ‘circular construction problem’ and the problem of an ‘explosion of complexity’ in a pure-feedback system. The resulting closed-loop system consists of a controller-filter pair, which satisfies the ISPS property, providing the celebrated small-gain theorem can be exploited to guarantee the stability of the closed-loop system. Referring to the issue of non-linearly parameterized uncertainty, adaptive laws are derived via the parameter separation technique. Numerical simulations are included to illustrate the effectiveness of the proposed control scheme.

Integrated guidance and control for dual-control missiles based on small-gain theorem

An integrated guidance and control (IGC) design approach is proposed based on small-gain theorem for missiles steered by both canard and tail controls. The angle of attack and pitch rate commands, which are aimed at producing desired aerodynamic lift to achieve robust tracking of a maneuvering target, are generated by a guidance law that is designed using input-to-state stability (ISS) theory. An IGC law is developed utilizing generalized small-gain theorem to enforce the commands, and it can be shown that both the line-of-sight (LOS) rate and the tracking error are input-to-state practically stable (ISpS) with respect to target maneuvers and missile model uncertainties. The algorithm is tested using computer simulations against a maneuvering target.

Design and input-to-state practically stable analysis of the mixed H2/H∞ feedback robust model predictive control

In this study, the authors address the problem of the mixed H2/H∞ robust model predictive control (RMPC) for a class of discrete-time systems with structured uncertainty and disturbances. The conditions of RMPC are given to satisfy both the H2 and H∞ performance requirements. In order to reduce the conservativeness caused by an unique feedback control law, a multi-step control strategy is introduced to improve the control performance and enlarge the feasible region of RMPC. Furthermore, an efficient version of the proposed RMPC is also given to reduce the online computational burden, which makes the design more practical. The proposed RMPCs are proven to be input-to-state practically stable (ISpS). A numerical example illustrates the effectiveness of the proposed designs.

Switched seesaw control for the stabilization of underactuated vehicles

This paper addresses the stabilization of a class of nonlinear systems in the presence of disturbances, using switching controllers. To this effect we introduce two new classes of switched systems and provide conditions under which they are input-to-state practically stable (ISpS). By exploiting these results, a methodology for control systems design—called switched seesaw control—is obtained that allows for the development of nonlinear control laws yielding input-to-state stability. The range of applicability and the efficacy of the methodology proposed are illustrated via two nontrivial design examples. Namely, stabilization of the extended nonholonomic double integrator (ENDI) and stabilization of an underactuated autonomous underwater vehicle (AUV) in the presence of input disturbances and measurement noise.

Semiglobal ISpS Disturbance Attenuation With Output Tracking via Direct Adaptive Design

Direct adaptive partial state feedback control is presented to achieve semiglobally input-to-state practically stable (ISpS) disturbance attenuation with output tracking for a class of uncertain time-varying nonlinear systems in which the unmeasured dynamics do not possess a constant disturbance attenuation level (CDAL). Identifying a necessary condition for the existence of a CDAL, direct adaptive neural networks (NNs) control is developed, where the universal approximation property of NNs and the domination design are employed together to overcome the difficulties due to the lack of state information, unknown system nonlinearities, and unknown state-dependent disturbance attenuation gain. The proposed method is coherent in the sense that it is applicable to the case in which a CDAL exists.