Two types of nonlinear control algorithms are presented for uncertain linear plants. Controllers of the first type are stabilizing polynomial feedbacks that allow to adjust a guaranteed convergence time of system trajectories into a prespecified neighborhood of the origin independently on initial conditions. The control design procedure uses block control principles and finite-time attractivity properties of polynomial feedbacks. Controllers of the second type are modifications of the second order sliding mode control algorithms. They provide global finite-time stability of the closed-loop system and allow to adjust a guaranteed settling time independently on initial conditions. Control algorithms are presented for both single-input and multi-input systems. Theoretical results are supported by numerical simulations.

https://hal.inria.fr/hal-00757561/document

Nonlinear Feedback Design for Fixed-Time Stabilization of Linear Control Systems

This paper recalls a few past achievements in Model Predictive Control, gives an overview of some current developments and suggests a few avenues for future research.

Model Predictive Control

Robust stability and control for systems that combine continuous-time and discrete-time dynamics. This article is a tutorial on modeling the dynamics of hybrid systems, on the elements of stability theory for hybrid systems, and on the basics of hybrid control. The presentation and selection of material is oriented toward the analysis of asymptotic stability in hybrid systems and the design of stabilizing hybrid controllers. Our emphasis on the robustness of asymptotic stability to data perturbation, external disturbances, and measurement error distinguishes the approach taken here from other approaches to hybrid systems. While we make some connections to alternative approaches, this article does not aspire to be a survey of the hybrid system literature, which is vast and multifaceted.

Hybrid dynamical systems

Cyber-physical systems integrate computation, communication, and physical capabilities to interact with the physical world and humans. Besides failures of components, cyber-physical systems are prone to malignant attacks, and specific analysis tools as well as monitoring mechanisms need to be developed to enforce system security and reliability. This paper proposes a unified framework to analyze the resilience of cyber-physical systems against attacks cast by an omniscient adversary. We model cyber-physical systems as linear descriptor systems, and attacks as exogenous unknown inputs. Despite its simplicity, our model captures various real-world cyber-physical systems, and it includes and generalizes many prototypical attacks, including stealth, (dynamic) false-data injection and replay attacks. First, we characterize fundamental limitations of static, dynamic, and active monitors for attack detection and identification. Second, we provide constructive algebraic conditions to cast undetectable and unidentifiable attacks. Third, by using the system interconnection structure, we describe graph-theoretic conditions for the existence of undetectable and unidentifiable attacks. Finally, we validate our findings through some illustrative examples with different cyber-physical systems, such as a municipal water supply network and two electrical power grids.

Attack Detection and Identification in Cyber-Physical Systems -- Part I: Models and Fundamental Limitations

We propose a robust data-driven model predictive control (MPC) scheme to control linear time-invariant systems. The scheme uses an implicit model description based on behavioral systems theory and past measured trajectories. In particular, it does not require any prior identification step, but only an initially measured input–output trajectory as well as an upper bound on the order of the unknown system. First, we prove exponential stability of a nominal data-driven MPC scheme with terminal equality constraints in the case of no measurement noise. For bounded additive output measurement noise, we propose a robust modification of the scheme, including a slack variable with regularization in the cost. We prove that the application of this robust MPC scheme in a multistep fashion leads to practical exponential stability of the closed loop w.r.t. the noise level. The presented results provide the first (theoretical) analysis of closed-loop properties, resulting from a simple, purely data-driven MPC scheme.

Data-Driven Model Predictive Control With Stability and Robustness Guarantees

Control of turbocharged diesel engines is a challenging task due to system nonlinearities and constraints on the inputs and process variables In this paper nonlinear model predictive control is applied to control a diesel engine with a variable geometry turbocharger and an exhaust gas recirculation valve The overall control objective is to regulate the setpoints of the air-fuel ratio and the amount of recirculated exhaust gas in order to obtain low exhaust emission values and low fuel consumption without smoke generation Simulation results are presented to study the advantages and disadvantages of nonlinear model predictive control The achieved performance is compared in simulations with a linear state feedback controller and an input-output linearization based control method As shown, nonlinear model predictive control achieves good overall control performance and constraint satisfaction

Nonlinear model predictive control of a turbocharged diesel engine

This paper presents a new observer design for Lipschitz nonlinear continuous-time systems with nonuniformly sampled measurements. Based on recent results in sampled-data control of linear continuous-time systems, linear matrix inequality (LMI) conditions are established to guarantee global stability of the estimation error dynamics and to design the observer matrix. The applicability of the proposed observer is demonstrated via two examples, that are the flexible joint robotic arm and Chua's circuit.

Observer with sample-and-hold updating for Lipschitz nonlinear systems with nonuniformly sampled measurements

There are well-known theoretical examples that show that stability constraints in nonlinear model predictive control (NMPC) are necessary in order to guarantee closed loop stability In this paper it is shown that these stability constraints, derived from theory, are also essential in practice In particular, an experimental study is carried out on a four tank system that illustrates the stability behavior of NMPC

Nonlinear model predictive control of a four tank system: An experimental stability study

This paper presents new observers for Lipschitz nonlinear systems, for systems with nondecreasing nonlinearities, and for linear systems. The dynamics of these observers exhibits impulsive dynamical behavior due to the update of the observer state at discrete instants of time. Conditions are given to ensure global convergence of these observers and possible applications are discussed. Furthermore, several approaches are proposed to design the observer matrices via linear matrix inequality (LMI) techniques. Finally, the proposed impulsive observer for Lipschitz nonlinear systems is applied to estimate the system state of a flexible joint robotic arm.

Observers with impulsive dynamical behavior for linear and nonlinear continuous-time systems

This paper presents a new observer for the class of linear continuous-time systems. In contrast to many well-established observers, which normally estimate the system state in an asymptotic fashion, the proposed observer estimates the exact system state in predetermined finite time. The finite convergence time of the proposed observer is achieved by updating the observer state based on current observer data at a definite time instant. Simulation results are presented to illustrate the convergence behavior of the proposed observer.

Tobias Raff

Papers

Nonlinear model predictive control of a turbocharged diesel engine

Observer with sample-and-hold updating for Lipschitz nonlinear systems with nonuniformly sampled measurements

Nonlinear model predictive control of a four tank system: An experimental stability study

Observers with impulsive dynamical behavior for linear and nonlinear continuous-time systems

An impulsive observer that estimates the exact state of a linear continuous-time system in predetermined finite time