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This paper describes a fast optimization algorithm for Model Predictive Control (MPC) with soft constraints. The method relies on the Kreisselmeier-Steinhauser function to provide a smooth approximation of the penalty function for a soft constraint. By introducing this approximation directly into the objective of an interior point optimization, there is no need for additional slack variables to capture...
In this paper, we present a novel linear model predictive control (MPC) scheme that relies on a continuous-time, barrier function based algorithm which asymptotically tracks the solution of a time-varying open-loop optimal control problem. In particular, the control input is obtained as the sampled output of a continuous-time dynamical system and no iterative optimization algorithm is needed in the...
Model predictive control (MPC) is an acclaimed method for the control of constrained systems. Since a constrained optimization problem has to be solved in every time step, the online computational effort of MPC is high. Explicit MPC provides an analytical solution to the same optimization problem, but explicit MPC is only useful for small systems, since the storage requirements for the explicit control...
This paper presents an infinite-dimensional Receding Horizon Observer for linear 2×2 hyperbolic systems with boundary measurements. The initial state is estimated as the optimal solution of an optimization problem which minimizes the distance between the measurements and the observer output. A constructive method is used to derive the existence and uniqueness of the solution. A composite strategy...
We describe an approximate dynamic programming method for stochastic control problems on infinite state and input spaces. The optimal value function is approximated by a linear combination of basis functions with coefficients as decision variables. By relaxing the Bellman equation to an inequality, one obtains a linear program in the basis coefficients with an infinite set of constraints. We show...
In this paper, we present a novel algorithm for estimating eigenvalues of the Laplacian matrix associated with the graph describing the network topology of a multi-agent system or a wireless sensor network. As recently shown, the average consensus matrix can be written as a product of Laplacian based consensus matrices whose stepsizes are given by the inverse of the nonzero Laplacian eigenvalues....
We consider convex optimization problems with N randomly drawn convex constraints. Previous work has shown that the tails of the distribution of the probability that the optimal solution subject to these constraints will violate the next random constraint, can be bounded by a binomial distribution. In this paper we extend these results to the violation probability of convex combinations of optimal...
To analyze a non linear closed loop which represents a high order aeroelastic model of a large civil aircraft interconnected with non-linearities, an Integral Quadratic Constraints (IQC) approach has been involved. This approach is particularly interesting for two reasons. The first one is that it is possible with the same stability criterion to analyze a large class of stability problems. And the...
The Multi-Parametric Toolbox is a collection of algorithms for modeling, control, analysis, and deployment of constrained optimal controllers developed under Matlab. It features a powerful geometric library that extends the application of the toolbox beyond optimal control to various problems arising in computational geometry. The new version 3.0 is a complete rewrite of the original toolbox with...
This paper proposes a simple model predictive control scheme for linear systems, tracking a random reference and analysis its performance. In such situations it is usual to assume that the reference eventually converges to a constant in which case convergence to zero of the tracking error can be established. In this note we characterize the set to which the tracking error converges and the associated...
Parameter-dependent constrained optimization problems like they occur in the context of model predictive control (MPC) can be solved explicitly by means of multi-parametric quadratic programming (mpQP) techniques. We present a complexity analysis for a recently proposed combinatorial mpQP algorithm and discuss its advantages over existing geometric approaches concerning off-line explicit MPC computations...
In this work we illustrate how approximate dynamic programing can be utilized to address problems of stochastic reachability in infinite state and control spaces. In particular we focus on the reach-avoid problem and approximate the value function on a linear combination of radial basis functions. In this way we get significant computational advantages with which we obtain tractable solutions to problems...
In order to deal with the control of large-scale infrastructures, a multi-level approach may be required in which several groups of decision makers have different objectives. A game formulation can help to structure such a control task. The reverse Stackelberg game has a hierarchical structure in which the follower player acts subsequent to the leader's disclosure of her leader function, which maps...
In this paper we employ general linear dynamic filters to robustly isolate faults in linear systems. The concept can be regarded as a generalization of observer based approaches and offers more degrees of freedom and less structural constraints than fault isolation observers (FIOs). We propose an LMI-based design approach for fault isolation filters (FIFs), where the existence of a solution for exactly...
Optimal control is recognized by the Airborne Wind Energy (AWE) community as a crucial tool for the development of the AWE industry. More specifically, the optimization of AWE systems for power generation is required to achieve the performance needed for their industrial viability. Models for AWE systems are highly nonlinear coupled systems. As a result, the optimization of power generation based...
We exploit the controllable canonical form of single-input linear parameter-varying (LPV) systems to synthesize explicit Model Predictive Control (MPC) feedback laws. The nonlinear state-parameter dependence is first moved into the feedback term, followed by devising a suitable input constraint set. This allows the MPC problem to be formulated with a quadratic performance index, avoiding costly dynamic...
Considering a constrained discrete-time linear time-varying system, this paper proposes a novel approach which aims at achieving high performance and enlarging the domain of attraction with respect to any particular linear controller. The main idea of the paper is to use a linear decomposition principle together with a parameter dependent Lyapunov function. At each time instant a quadratic programming...
We consider a control design problem aimed at balancing quadratic performance of linear systems with additional requirements on the control signal. These are introduced in order to obtain controls that are either sparse or infrequently changing in time. To achieve this objective, we augment a standard quadratic performance index with an additional term that penalizes either the ℓ1 norm or the total...
In this paper, we provide a systematic convex programming-based approach for the optimal locations of static actuators and sensors for the control of nonequilibrium dynamics. The problem is motivated with regard to its application for control of nonequilibrium dynamics in the form of temperature in building systems and control of oil spill in oceanographic flow. The controlled evolution of a passive...
In this paper, we present a procedure for finding the best LFT uncertainty model by minimizing the ℌ -infinity norm of the uncertainty set with respect to a nominal model subject to known input-output data. The main problem is how to express the data-matching constraints for convenient use in the optimization problem. For some uncertainty structures, they can readily be formulated as a set of linear...
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