Hossein Beikzadeh

Multirate Output Feedback Control of Nonlinear Networked Control Systems

This technical note studies output feedback stabilization of nonlinear networked control systems (NCSs) under multirate sampling. Network induced constraints are modeled as norm-bounded uncertainties and a general framework for multirate nonlinear NCS design is established. Under standard continuity and consistency assumptions, we analyze dissipativity of the proposed multirate output feedback structure in the presence of channels uncertainties and disturbance inputs. Our result is then applied to preserve input-to-state stability (ISS) in a semiglobal practical sense and also to derive sufficient conditions that guarantee exponential stability of the uncertain multirate NCS in the absence of disturbances.

Multirate Observers for Nonlinear Sampled-Data Systems Using Input-to-State Stability and Discrete-Time Approximation

This paper is devoted to the problem of nonlinear state estimation under multirate sampling in presence of disturbance inputs. Considering a general description of a nonlinear sampled-data system, we establish a prescriptive framework for multirate observer design via an approximate discrete-time model of the plant. This framework is shown to be input-to-state stable in a semiglobal practical sense with respect to the estimation error for the unknown exact discrete-time model. A numerical example of an aerospace vehicle with input and output channels of various sampling rates demonstrates how the multirate observer can drastically improve performance compared with the single-rate observer.

Input-to-error stable observer for nonlinear sampled-data systems with application to one-sided Lipschitz systems

In this paper the design of sampled-data state observers for nonlinear plants is investigated under the effect of system and measurement disturbance signals. We establish general design principles using the standard approaches of (i) direct discrete-time design via approximation and (ii) discretization of a continuous-time observer (emulation). By interpreting the disturbances as exogenous inputs affecting the error dynamics, sufficient conditions are derived which ensure the input-to-state stability (ISS) of the observer error system in a semiglobal practical sense for the unknown exact discrete-time model. Next, we focus on systems whose vector fields are one-sided Lipschitz to develop constructive design techniques via linear matrix inequalities (LMIs). Numerical simulations of an academic example and a chaotic attractor corroborate the effectiveness of the proposed sampled-data estimators.

Robust SDRE filter design for nonlinear uncertain systems with an H∞ performance criterion

In order to remedy the effects of modeling uncertainty, measurement noise and input disturbance on the performance of the standard state-dependent Riccati equation (SDRE) filter, a new robust H(∞) SDRE filter design is developed in this paper. Based on the infinity-norm minimization criterion, the proposed filter effectively estimates the states of nonlinear uncertain system exposed to unknown disturbance inputs. Moreover, by assuming a mild Lipschitz condition on the chosen state-dependent coefficient form, fulfillment of a modified H(∞) performance index is guaranteed in the proposed filter. The effectiveness of the robust SDRE filter is demonstrated through numerical simulations where it brilliantly outperforms the conventional SDRE filter in presence of model uncertainties, disturbance and measurement noise, in terms of estimation error and region of convergence.

Nonlinear sensorless speed control of PM synchronous motor via an SDRE observer-controller combination

In this paper, a nonlinear control approach for permanent magnet synchronous motor (PMSM) drives, without mechanical sensors, is presented. The proposed method is based on a combination of the well-known nonlinear regulation technique, state-dependent Riccati equation (SDRE), and its filtering counterpart (SDREF) which is derived by constructing the dual of this control method. The SDREF is designed for online estimation of the rotor speed, position and also the load torque by only measuring the motor voltages and currents. The estimated values are applied in the controller structure as state variables. We demonstrate the performance and applicability of this new nonlinear control for PMSM derives by an illustrative simulation in presence of variable load torque. The sensitivity and robustness of the proposed method are also investigated for the motor parameters variations.

Stability analysis of the discrete-time difference SDRE state estimator in a noisy environment

The state-dependent Riccati equation filter (SDREF) is a recent nonlinear estimation technique which has yielded a number of impressive results. However, the theoretical investigations of the filter have been carried out only in a deterministic environment. In this paper a discrete time difference SDRE-based observer for general nonlinear systems in a stochastic framework is considered, and its error behavior has been also analyzed. It is proved that, the estimation error remains bounded in mean square if the system to be observed satisfies certain conditions, and both the initial estimation error and the disturbing noise terms are small enough. Moreover, the results are verified thorough a simulation study of an example system.

Robust H ∞ filtering for nonlinear uncertain systems using state-dependent riccati equation technique

The standard state-dependent Riccati equation (SDRE) filter, which is set up by direct SDC parameterization, demands complete knowledge of the system model, and the disturbance inputs characteristics. However, this inherent dependency can severely degrade its performance in practical applications. In this paper, based on the H∞ norm minimization criterion, a robust SDRE filter is proposed to effectively estimate the states of nonlinear uncertain systems exposed to unknown disturbance inputs. Considering a Lipschitz condition on the chosen SDC form, we guarantee fulfillment of a modified H∞ performance index by the proposed filter. The effectiveness of the robust SDRE filter is demonstrated through numerical simulations where it brilliantly outperforms the usual SDRE filters in presence of model uncertainties as well as process and measurement noises.

Observer-based H ∞ control using the incremental gain for one-sided Lipschitz nonlinear systems

In this paper, an H∞ output feedback controller is presented for one-sided Lipschitz systems, which consists of a state feedback control together with a nonlinear observer. By proposing the L2 incremental gain as an alternative H∞ performance measure to the usual gain, we develop a design technique that guarantees an asymptotically stable closed-loop system in the absence of disturbance inputs and further minimizes the incremental gain from disturbances to the controlled output. This method is based on the Lyapunov function parametrization and is formulated in terms of linear matrix inequalities (LMIs). Our result is then validated via numerical example of a discontinuous plant exposed to disturbance inputs with numerous variations.

Robust Sampled-Data Bilateral Teleoperation: Single-Rate and Multirate Stabilization

This paper investigates robust sampled-data control design strategies for nonlinear bilateral teleoperators exposed to communication constraints, using discrete-time approximate models of the master and slave robots and assuming both single-rate and multirate sampling. The single-rate design guarantees input-to-state stability of the (unknown) exact discrete-time model in a semiglobal practical sense, in spite of norm-bounded channel uncertainties. Then imposing different sampling rates on positions/velocities or torque inputs in each side of the system, a multirate scheme is proposed and shown to maintain similar stability properties under a well-known Nyquist frequency assumption on control torques. Simulation results verify the advantages of our direct sampled-data design. The example also shows that the multirate controller successfully stabilizes the teleoperation system even when the single-rate bilateral setup is ineffective in the presence of different sampling rates.

Sampled-data observer for one-sided Lipschitz systems: Single-rate and multirate cases

The problem of sampled-data observer design is addressed for the so-called nonlinear systems with one sided Lipschitz nonlinearity in presence of disturbance inputs. We first develop a single-rate observer using a refined Euler model formulated via tractable linear matrix inequalities (LMIs). This scheme is shown to be input-to-state stable from exogenous disturbances to the estimation error in a semiglobal practical sense for the unknown exact discrete-time plant model. Then, the proposed observer is modified appropriately to cope with the practical case of multirate sampling by preserving similar stability property. A simulation example justifies the efficiency of both observers for the one-sided Lipschitz systems and demonstrates the superiority of the multirate observer when the input and output signals are sampled at different rates.