Daniel Simon

Reference Tracking MPC Using Dynamic Terminal Set Transformation

Among the many different formulations of Model Predictive Control (MPC) with guaranteed stability, one that has attracted significant attention is the formulation with a terminal cost and terminal constraint set, the so called dual mode formulation.

Reference tracking MPC using terminal set scaling

A common assumption when proving stability of linear MPC algorithms for tracking applications is to assume that the desired setpoint is located far into the interior of the feasible set. The reason for this is that the terminal state constraint set which is centered around the setpoint must be contained within the feasible set. In many applications this assumption can be severely limiting since the terminal set is relatively large and therefore limits how close the setpoint can be to the boundary of the feasible set. We present simple modifications that can be performed in order to guarantee stability and convergence to setpoints located arbitrarily close to the boundary of the feasible set. The main idea is to introduce a scaling variable which dynamically scales the terminal state constraint set and therefore allows a setpoint to be located arbitrarily close to the boundary. In addition to this the concept of pseudo setpoints is used to gain the maximum possible region of attraction and to handle infeasible references. Recursive feasibility and convergence to the desired setpoint, or its closest feasible alternative, is proven and a motivating example of controlling an agile fighter aircraft is given.

Feedback Control as MAPE-K loop in Autonomic Computing

Computing systems are becoming more and more dynamically reconfigurable or adaptive, to be flexible w.r.t. their environment and to automate their administration. Autonomic computing proposes a general structure of feedback loop to take this into account. In this paper, we are particularly interested in approaches where this feedback loop is considered as a case of control loop where techniques stemming from Control Theory can be used to design efficient safe, and predictable controllers. This approach is emerging, with separate and dispersed effort, in different areas of the field of reconfigurable or adaptive computing, at software or architecture level. This paper surveys these approaches from the point of view of control theory techniques, continuous and discrete (supervisory), in their application to the feedback control of computing systems, and proposes detailed interpretations of feedback control loops as MAPE-K loop, illustrated with case studies.

Stability analysis of model predictive controllers using Mixed Integer Linear Programming

It is a well known fact that finite time optimal controllers, such as MPC do not necessarily result in closed loop stable systems. Within the MPC community it is common practice to add a final state constraint and/or a final state penalty in order to obtain guaranteed stability. However, for more advanced controller structures it can be difficult to show stability using these techniques. Additionally in some cases the final state constraint set consists of so many inequalities that the complexity of the MPC problem is too big for use in certain fast and time critical applications. In this paper we instead focus on deriving a tool for a-postiori analysis of the closed loop stability for linear systems controlled with MPC controllers. We formulate an optimisation problem that gives a sufficient condition for stability of the closed loop system and we show that the problem can be written as a Mixed Integer Linear Programming Problem (MILP).

Command Governor Approach to Maneuver Limiting in Fighter Aircraft

Modern fighter aircraft require maximum control performance in order to have the upper hand in a dogfight or when they have to outmaneuver an enemy missile. Therefore pilots must be able to maneuver the aircraft very close to the limit of what it is capable of while at the same time focus on the tactical tasks of the mission. To enable this, modern flight control systems have automatic systems for angle of attack and load factor limiting. These types of systems can utilize predictions of the aircraft response to pilot inputs and alter the properties of the closed loop system to minimize the predicted overshoot. Two such design techniques are model predictive control and reference and command governors. Model predictive controllers are most often used as inner loop feedback controllers which alter the control signal as function of the predicted output while reference and command governors are applied in an outer feedback loop around a nominal controller. There can be several benefits from using reference and command governors compared to model predictive controllers. First, the governors can be used as add-ons to existing legacy controllers so there is no need to redo the complete design. Furthermore the nominal inner loop controller can be tuned to achieve good performance in the nominal case, e.g., use nonlinear feedbacks to linearize the closed loop system, and the governor focus on the maneuver limiting task. It also gives a good modularity such that one can replace parts of the control system without the need to redo all of the design. Last but not least from a flight safety perspective it might be easier to certify optimization algorithms running in an outer loop which can be turned off in case of failures without affecting stability. While model predictive controllers have been extensively investigated for flight control applications [1–28] most of them consider reconfigurable flight control systems and only few focus on envelope protection and maneuver limiting [7, 13, 17, 21]. Even though reference governors have been subject to research for quite some time very little research has been performed on applying reference and command governors to flight control design and maneuver limiting [23, 29–33]. Most of these papers consider simplified conditions with only a single linear or nonlinear system and no complex simulation environments. In the papers by Petersen et al. [23] and Zinnecker et al. [29] the authors apply reference governors to the control of hypersonic vehicle. In the paper by Zinnecker the focus is mainly on input constraints. Kolmanovsky and Kahveci [30] uses a reference governor to handle control actuator limitations of a UAV glider and compare this to an adaptive anti-windup scheme and in the paper by Martino [31] the author investigates command governors for handling amplitude and rate constraints on a small commercial aircraft. The authors, Ye et al. [32], investigate reference governors for maneuver limiting in high angle of attack maneuvers. They investigate and compare static and dynamic reference governors with a reference governor structure based on a step response

Angle of Attack and Load Factor Limiting in Fighter Aircraft using Command Governors

Modern fighter aircraft require maximum control performance in order to have the upper hand in a dogfight or when they have to outmaneuver an enemy missile. Therefore pilots must be able to maneuve ...