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Stabilizing Model Predictive Control of Hybrid Systems
"... Abstract—In this note, we investigate the stability of hybrid systems in closedloop with model predictive controllers (MPC). A priori sufficient conditions for Lyapunov asymptotic stability and exponential stability are derived in the terminal cost and constraint set fashion, while allowing for dis ..."
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Cited by 46 (31 self)
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Abstract—In this note, we investigate the stability of hybrid systems in closedloop with model predictive controllers (MPC). A priori sufficient conditions for Lyapunov asymptotic stability and exponential stability are derived in the terminal cost and constraint set fashion, while allowing for discontinuous system dynamics and discontinuous MPC value functions. For constrained piecewise affine (PWA) systems as prediction models, we present novel techniques for computing a terminal cost and a terminal constraint set that satisfy the developed stabilization conditions. For quadratic MPC costs, these conditions translate into a linear matrix inequality while, for MPC costs based on 1,norms, they are obtained as norm inequalities. New ways for calculating low complexity piecewise polyhedral positively invariant sets for PWA systems are also presented. An example illustrates the developed theory. Index Terms—Hybrid systems, Lyapunov stability, model predictive control (MPC), piecewise affine systems. I.
Feedback Thermal Control for Realtime Systems
"... Abstract: Thermal control is crucial to realtime systems as excessive processor temperature can cause system failure or unacceptable performance degradation due to hardware throttling. Realtime systems face significant challenges in thermal management as they must avoid processor overheating while ..."
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Cited by 12 (2 self)
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Abstract: Thermal control is crucial to realtime systems as excessive processor temperature can cause system failure or unacceptable performance degradation due to hardware throttling. Realtime systems face significant challenges in thermal management as they must avoid processor overheating while still delivering desired realtime performance. Furthermore, many realtime systems must handle a broad range of uncertainties in system and environmental conditions. To address these challenges, this paper presents Thermal Control under Utilization Bound (TCUB), a novel thermal control algorithm specifically designed for realtime systems. TCUB employs a feedback control loop that dynamically controls both processor temperature and CPU utilization through task rate adaptation. Rigorously modeled and designed based on control theory, TCUB can maintain both desired processor temperature and CPU utilization, thereby avoiding processor overheating and maintaining desired realtime performance. A salient feature of TCUB lies in its capability to handle a broad range of uncertainties in terms of processor power consumption, task execution times, ambient temperature, and unexpected thermal faults. The robustness of TCUB makes it particularly suitable for realtime embedded systems that must operate in highly unpredictable and hash environments. The advantages of TCUB have been demonstrated through extensive simulations under a broad range of system and environmental uncertainties.
Lyapunov functions, stability and inputtostate stability subtleties for discretetime discontinuous systems
 IEEE Transactions on Automatic Control
, 2009
"... Abstract—In this note we consider stability analysis of discretetime discontinuous systems using Lyapunov functions. We demonstrate via simple examples that the classical second method of Lyapunov is precarious for discretetime discontinuous dynamics. Also, we indicate that a particular type of Ly ..."
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Cited by 8 (6 self)
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Abstract—In this note we consider stability analysis of discretetime discontinuous systems using Lyapunov functions. We demonstrate via simple examples that the classical second method of Lyapunov is precarious for discretetime discontinuous dynamics. Also, we indicate that a particular type of Lyapunov condition, slightly stronger than the classical one, is required to establish stability of discretetime discontinuous systems. Furthermore, we examine the robustness of the stability property when it was attained via a discontinuous Lyapunov function, which is often the case for discretetime hybrid systems. In contrast to existing results based on smooth Lyapunov functions, we develop several inputtostate stability tests that explicitly employ an available discontinuous Lyapunov function.
LowComplexity Polynomial Approximation of Explicit MPC via Linear Programming
, 2010
"... This paper addresses the issue of the ..."
Global inputtostate stability and stabilization of discretetime piecewise affine systems
 HYBRID SYSTEMS
, 2008
"... This paper presents sufficient conditions for global InputtoState (practical) Stability (ISpS) and stabilization of discretetime, possibly discontinuous, PieceWise Affine (PWA) systems. Piecewise quadratic candidate ISpS (ISS) Lyapunov functions are employed for both analysis and synthesis pur ..."
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Cited by 4 (2 self)
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This paper presents sufficient conditions for global InputtoState (practical) Stability (ISpS) and stabilization of discretetime, possibly discontinuous, PieceWise Affine (PWA) systems. Piecewise quadratic candidate ISpS (ISS) Lyapunov functions are employed for both analysis and synthesis purposes. This enables us to obtain sufficient conditions based on linear matrix inequalities, which can be solved efficiently. One of the advantages of using the ISpS framework is that the additive disturbance inputs are explicitly taken into account in the analysis and synthesis procedures, and the results apply to PWA systems in their full generality, i.e. nonzero affine terms are allowed in the regions in the partition whose closure contains the origin.
Optimized inputtostate stabilization of discretetime nonlinear systems with bounded inputs
 In American Control Conference
, 2008
"... Abstract — In the problem of inputtostate stabilization of nonlinear systems, synthesis of inputtostate stabilizing feedback laws is usually carried out offline. This results in a constant inputtostate stability (ISS) gain, which is guaranteed for the closedloop system. As an alternative, we ..."
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Cited by 3 (1 self)
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Abstract — In the problem of inputtostate stabilization of nonlinear systems, synthesis of inputtostate stabilizing feedback laws is usually carried out offline. This results in a constant inputtostate stability (ISS) gain, which is guaranteed for the closedloop system. As an alternative, we propose a finite dimensional optimization problem that allows for the simultaneous online computation of an ISS control action, and minimization of the ISS gain of the closedloop system. The advantages of the developed controller are: ISS is guaranteed for any (feasible) solution of the optimization problem, constraints can be explicitly accounted for and feedback to disturbances is provided actively, online. The control scheme also has favorable computational properties for nonlinear systems affine in control. In this case the optimization problem can be formulated as a single quadratic or linear program. I.
Observer Design for Motorcycle’s Lean and Steering Dynamics Estimation: a TakagiSugeno Approach
, 2013
"... Abstract — In this paper, a nonlinear motorcycle model is considered in order to estimate both the lean and steering dynamics. The model is transformed into a TakagiSugeno (TS) form using the wellknown sector nonlinearity approach. The first contribution of this work is the exactness of the obtai ..."
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Cited by 2 (2 self)
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Abstract — In this paper, a nonlinear motorcycle model is considered in order to estimate both the lean and steering dynamics. The model is transformed into a TakagiSugeno (TS) form using the wellknown sector nonlinearity approach. The first contribution of this work is the exactness of the obtained TS model compared to the considered nonlinear model, where the weighting functions of the TS model depend on unmeasured state variables. A novel approach to construct a nonlinear unknown input fast observer is proposed. The objective is the simultaneous reconstruction of the state variables and the rider’s torque. The observer’s convergence is studied using Lyapunov theory guaranteeing boundedness of the state and unknown input estimation errors which is expressed by the Input to State Practical Stability (ISpS). Stability conditions are then expressed in terms of Linear Matrix Inequalities (LMI). Finally, simulation results are provided to confirm the suitability of the proposed nonlinear observer. I.
Observerbased Control of Discretetime Piecewise Affine Systems: Exploiting Continuity Twice
"... Abstract — Outputbased feedback control of discretetime hybrid systems is an important problem, as in practice it is rarely the case that the full state variable is available for feedback. A typical approach for outputbased feedback design for linear and smooth nonlinear systems is to use certain ..."
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Abstract — Outputbased feedback control of discretetime hybrid systems is an important problem, as in practice it is rarely the case that the full state variable is available for feedback. A typical approach for outputbased feedback design for linear and smooth nonlinear systems is to use certainty equivalence control, in which an observer and a state feedback controller (using the observer state) are combined. Although for linear systems and some classes of nonlinear systems, separation principles exist to justify this approach, for hybrid systems this is not the case. In this paper, we isolate a class of hybrid systems for which a systematic design procedure for certainty equivalence controllers including a separation principle will be presented. This class consists of discretetime piecewiseaffine (PWA) systems with continuous dynamics. In the design procedure, we will exploit the continuity of the PWA dynamics twice. Firstly, it will be used to establish inputtostate stability (ISS) w.r.t. measurement errors from ISS w.r.t. additive disturbances. This is a crucial step as the latter problem is much easier to tackle than the former. Secondly, continuity will be used in the observer design procedure to obtain a significantly simplified set of LMIs with respect to existing observer design approaches for PWA systems. All the design conditions will be formulated in term of LMIs, which can be solved efficiently, as is also illustrated by a numerical example. Index Terms — Hybrid systems, PWA systems, inputtostate stability, separation principle
Robust nonlinear model predictive control of a runofmine ore milling circuit
 IEEE Trans. Control Syst. Technol
, 2010
"... Abstract—This brief investigates the feasibility of applying a robust nonlinear model predictive controller to a runofmine ore milling circuit, and the conditions under which such a controller might be worthwhile implementing. The runofmine ore milling circuit model used consists of nonlinear m ..."
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Abstract—This brief investigates the feasibility of applying a robust nonlinear model predictive controller to a runofmine ore milling circuit, and the conditions under which such a controller might be worthwhile implementing. The runofmine ore milling circuit model used consists of nonlinear modules for the individual components of the milling circuit, allowing for arbitrary milling circuit configurations to be modeled. The model is cast into a robust nonlinear model predictive control framework, and a practically motivated simulation of the mill model being controlled by an robust nonlinear model predictive control (RNMPC) controller is presented. Issues related to implementing such a controller are investigated. Index Terms—Grinding mill, milling circuit, process control, robust nonlinear model predictive control (RNMPC), runofmine (ROM) ore. I.