A Robust Fault-Tolerant Predictive Control for Discrete-Time Linear Systems Subject to Sensor and Actuator Faults

Abstract

In this paper, a robust fault-tolerant model predictive control (RFTPC) approach is proposed for discrete-time linear systems subject to sensor and actuator faults, disturbances, and input constraints. In this approach, a virtual observer is first considered to improve the observation accuracy as well as reduce fault effects on the system. Then, a real observer is established based on the proposed virtual observer, since the performance of virtual observers is limited due to the presence of unmeasurable information in the system. Based on the estimated information obtained by the observers, a robust fault-tolerant model predictive control is synthesized and used to control discrete-time systems subject to sensor and actuator faults, disturbances, and input constraints. Additionally, an optimized cost function is employed in the RFTPC design to guarantee robust stability as well as the rejection of bounded disturbances for the discrete-time system with sensor and actuator faults. Furthermore, a linear matrix inequality (LMI) approach is used to propose sufficient stability conditions that ensure and guarantee the robust stability of the whole closed-loop system composed of the states and the estimation error of the system dynamics. As a result, the entire control problem is formulated as an LMI problem, and the gains of both observer and robust fault-tolerant model predictive controller are obtained by solving the linear matrix inequalities (LMIs). Finally, the efficiency of the proposed RFTPC controller is tested by simulating a numerical example where the simulation results demonstrate the applicability of the proposed method in dealing with linear systems subject to faults in both actuators and sensors.

Computationally Efficient Nonlinear Model Predictive Control Using the L1 Cost-Function

“…For example, when the measurement of lateral vehicle speed is not available, it can be estimated from other measurable parameters [ 10 ]. The study presented in [ 17 ] shows another approach of dealing with faulty sensors for linear systems by changing the representation of the process model. The work in [ 18 ] presents a real vehicle that uses an external camera to detect obstacles and lanes on the road as well as external rear-corner radars to detect objects coming from the rear.…”

Semi-Analytical Planetary Landing Guidance with Constraint Equations Using Model Predictive Control

“…where C d is the coefficient of drag and set to 0.5, ρ is the atmospheric density and set to 0.01 kg/m 3 , A ref is the drag reference area and set to 6 m 2 , and v wind is the velocity of the wind and set to [−5;−5;0] m/s. In addition, we add a horizontal acceleration to simulate the actual disturbances and possible faults [38], which is set as follows. When z < 5 m, the open-loop control mode is adopted.…”

“…Model predictive control (MPC) is a popular advanced method to control dynamical systems subject to uncertain disturbances and possible faults [36][37][38]. In Ref.…”

“…In Ref. [38], the sensor and actuator faults were considered and a robust fault-tolerant model predictive control approach was proposed. By minimizing the upper bound of the objective function, the MPC state feedback law is obtained in terms of linear matrix inequalities (LMIs).…”

A robustly stabilizing fault‐tolerant MPC: A performance improvement‐based approach

“…Depending on the type of uncertainty description, the robust MPC strategy can be tube‐based MPC, [ 17 ] stabilizing min‐max MPC scheme, [ 14 ] Lyapunov function‐based MPC, [ 18,19 ] and output feedback‐based MPC. [ 20 ] Recursive least squares, [ 17 ] comparison sets, [ 15 ] observer‐based state feedback, [ 21 ] and set membership [ 16 ] are the main identification methods used. With online identification, MPC algorithms must balance conflicting requirements between persistently exciting control inputs for the accuracy of the uncertainty model identification system and achieve improved control performance.…”