Masoud Abbaszadeh

Nonlinear observer design for one-sided Lipschitz systems

Control and state estimation of nonlinear systems satisfying a Lipschitz continuity condition have been important topics in nonlinear system theory for over three decades, resulting in a substantial amount of literature. The main criticism behind this approach, however, has been the restrictive nature of the Lipschitz continuity condition and the conservativeness of the related results. This work deals with an extension to this problem by introducing a more general family of nonlinear functions, namely one-sided Lipschitz functions. The corresponding class of systems is a superset of its well-known Lipschitz counterpart and possesses inherent advantages with respect to conservativeness. In this paper, first the problem of state observer design for this class of systems is established, the challenges are discussed and some analysis-oriented tools are provided. Then, a solution to the observer design problem is proposed in terms of nonlinear matrix inequalities which in turn are converted into numerically efficiently solvable linear matrix inequalities.

A Robust Observer Design Method for Continuous-Time Lipschitz Nonlinear Systems

A new observer design method for Lipschitz nonlinear systems is proposed in the form of LMI optimization problem. Besides asymptotic stability, the proposed observer is robust against some nonlinear uncertainty. In addition, a new LMI approach for Hinfin nonlinear observer designed is introduced. The new LMI formulation allows optimizations both on the Hinfin cost and nonlinear uncertainty robustness

LMI optimization approach to robust H ∞ filtering for discrete-time nonlinear uncertain systems

A new approach for the design of robust Hinfin filter for a class of discrete-time Lipschitz nonlinear systems with time-varying uncertainties is proposed based on linear matrix inequalities. Thanks to the linearity of the proposed LMIs in both the admissible Lipschitz constant of the system and the disturbance attenuation level, they can be simultaneously optimized through convex optimization. The resulting Hinfin observer guarantees exponential stability of the estimation error dynamics with guaranteed decay rate and is robust against time-varying parametric uncertainties. The proposed observer has also an extra important feature, robustness against nonlinear additive uncertainty. Explicit norm-wise and element- wise bounds on the tolerable nonlinear uncertainty are derived.

Robust static output feedback stabilization of discrete-time nonlinear uncertain systems with H ∞ performance

A new approach for the design of robust static output feedback controller for a class of discrete-time Lipschitz nonlinear systems with time-varying uncertainties is proposed based on linear matrix inequalities. The controller has also a guaranteed disturbance attenuation level (Hinfin performance). Thanks to the linearity of the proposed LMIs in both the admissible Lipschitz constant of the system and the disturbance attenuation level, they can be simultaneously optimized through convex multiobjective optimization. The optimization over Lipschitz constant adds an extra important and new feature to the controller, robustness against nonlinear uncertainty. The resulting controller is robust against both nonlinear additive uncertainty and time-varying parametric uncertainties. Explicit norm-wise and element-wise bounds on the tolerable nonlinear uncertainty are derived.

Nonlinear H-infinity control for 4-DOF underactuated overhead cranes:

The article proposes a nonlinear H-infinity control method for four degrees of freedom underactuated overhead cranes. The crane’s system is underactuated because it receives only two external inputs, namely a force that allows the motion of the bridge along the x-axis and a force that allows the motion of the trolley along the y-axis. A solution to the control problem of this underactuated system is obtained by applying nonlinear H-infinity control. The dynamic model of the overhead crane undergoes approximate linearization round local operating points which are redefined at each iteration of the control algorithm. These temporary equilibria consist of the last value of the crane’s state vector and of the last value of the control signal that was exerted on it. For the approximate linearization of the system’s dynamics, a Taylor series expansion is performed through the computation of the associated Jacobian matrices. The modelling errors are compensated by the robustness of the control algorithm. Next, for the linearized equivalent model of the crane an H-infinity feedback controller is designed. This requires the solution of an algebraic Riccati equation at each iteration of the computer control program. It is shown that the control scheme achieves H-infinity tracking performance, which implies maximum robustness to modelling errors and external perturbations. The stability of the control loop is proven through Lyapunov analysis.

Full-order and Reduced-order Exponential Observers for Discrete-time Nonlinear Systems with Incremental Quadratic Constraints

This paper investigates the observer design for a class of nonlinear discrete-time systems satisfying incremental quadratic constraints. A circle criterion based full-order observer is constructed by injecting output estimation error into the observer nonlinear terms. We also construct a reduced-order observer to estimate the unmeasured system state. The proposed observers guarantee exponential convergence of the estimation error to zero. The design of the proposed observers is reduced to solving a set of linear matrix inequalities. It is proved that the conditions under which a full-order observer exists also guarantee the existence of a reduced-order observer. Compared to some previous results in the literature, this work considers a larger class of nonlinearities and unifies some related observer designs for discrete-time nonlinear systems. Finally, a numerical example is given to illustrate the effectiveness of the proposed design.

Nonlinear H-infinity control for the rotary pendulum

The rotary (Furutas) pendulum is used to analyzed the performance of a new nonlinear optimal (H-infinity) control for underactuated robotic systems. After applying partial feedback linearization, the pendulums dynamic model is first transformed to an equivalent form. The later description of the pendulums dynamics undergoes approximate linearization which takes place round a temporary operating point (equilibrium) recomputed at each iteration of the control algorithm. The linearization makes use of Taylor series expansion of the state-space model of the system and of computation of the associated Jacobian matrices. For the approximately linearized model of the pendulum an H-infinity feedback controller is developed. Through the repetitive solution of an algebraic Riccati equation which is also performed at each step of the control method, the controllers gain is computed. The stability features of the control loop are proven with Lyapunov analysis. First it is shown that the control loop satisfies the H-infinity tracking performance condition. Next, under moderate conditions it is also shown that the global asymptotic stability of the control loop can be assured.

Cyber-attack detection and accommodation algorithm for energy delivery systems

Cyber-attack accommodation in a cyber-physical system is to ensure system operation, integrity and availability while maintaining a reasonable operational performance under attack. In this paper, we present a novel cyber-attack accommodation algorithm by estimating the true operational states of the system with new boundary & performance constrained resilient estimators while the system is continuously operating and is under attack. Our approach is based on combining data driven machine learning and physics based domain knowledge with traditional resilient estimation. The results were evaluated using a high fidelity model-based simulation environment.

Dynamical robust nonlinear H ∞ filtering for Lipschitz descriptor systems with parametric and nonlinear uncertainties

In this paper, a dynamical robust nonlinear Hinfin filtering method is proposed for a class of Lipschitz descriptor systems in which the nonlinearities appear in both the state and measured output equations. The system is assumed to have norm-bounded uncertainties in the realization matrices as well as nonlinear uncertainties. We synthesis the Hinfin observer through semidefinite programming and strict LMIs. The admissible Lipschitz constants of the nonlinear functions are maximized through LMI optimization. The resulting Hinfin observer guarantees asymptotic stability of the estimation error dynamics with prespecified disturbance attenuation level and is robust against time-varying parametric uncertainties as well as Lipschitz nonlinear additive uncertainty. Explicit bound on the tolerable nonlinear uncertainty is derived based on norm-wise robustness analysis.