8,981 research outputs found
Composing MPC with LQR and Neural Network for Amortized Efficiency and Stable Control
Model predictive control (MPC) is a powerful control method that handles
dynamical systems with constraints. However, solving MPC iteratively in real
time, i.e., implicit MPC, remains a computational challenge. To address this,
common solutions include explicit MPC and function approximation. Both methods,
whenever applicable, may improve the computational efficiency of the implicit
MPC by several orders of magnitude. Nevertheless, explicit MPC often requires
expensive pre-computation and does not easily apply to higher-dimensional
problems. Meanwhile, function approximation, although scales better with
dimension, still requires pre-training on a large dataset and generally cannot
guarantee to find an accurate surrogate policy, the failure of which often
leads to closed-loop instability. To address these issues, we propose a
triple-mode hybrid control scheme, named Memory-Augmented MPC, by combining a
linear quadratic regulator, a neural network, and an MPC. From its standard
form, we further derive two variants of such hybrid control scheme: one
customized for chaotic systems and the other for slow systems. The proposed
scheme does not require pre-computation and can improve the amortized running
time of the composed MPC with a well-trained neural network. In addition, the
scheme maintains closed-loop stability with any neural networks of proper input
and output dimensions, alleviating the need for certifying optimality of the
neural network in safety-critical applications.Comment: 13 pages, 10 figures, 2 table
Stability of hybrid model predictive control
In this paper we investigate the stability of hybrid systems in closed-loop with Model Predictive
Controllers (MPC) and we derive a priori sufficient conditions for Lyapunov asymptotic stability and
exponential stability. A general theory is presented which proves that Lyapunov stability is achieved for
both terminal cost and constraint set and terminal equality constraint hybrid MPC, even though the
considered Lyapunov function and the system dynamics may be discontinuous. For particular choices
of MPC criteria and constrained Piecewise Affine (PWA) systems as the prediction models we develop
novel algorithms for computing the terminal cost and the terminal constraint set. For a quadratic MPC
cost, the stabilization conditions translate into a linear matrix inequality while, for an 1-norm based
MPC cost, they are obtained as 1-norm inequalities. It is shown that by using 1-norms, the terminal
constraint set is automatically obtained as a polyhedron or a finite union of polyhedra by taking a
sublevel set of the calculated terminal cost function. New algorithms are developed for calculating
polyhedral or piecewise polyhedral positively invariant sets for PWA systems. In this manner, the on-line
optimization problem leads to a mixed integer quadratic programming problem or to a mixed integer
linear programming problem, which can be solved by standard optimization tools. Several examples
illustrate the effectiveness of the developed methodology
Non-smooth model predictive control: stability and applications to hybrid systems
In this report we investigate the stability of hybrid systems in closed-loop with Model Predictive Controllers (MPC) and we derive a priori sufficient conditions for Lyapunov asymptotic stability and exponential stability. A general theory is presented which proves that Lyapunov stability is achieved for both terminal cost and constraint set and terminal equality constraint hybrid MPC, even though the considered Lyapunov function and the system dynamics may be discontinuous. For particular choices of MPC criteria and constrained Piecewise Affine (PWA) systems as the prediction models we develop novel algorithms for computing the terminal cost and the terminal constraint set. For a quadratic MPC cost, the stabilization conditions translate into a linear matrix inequality while, for an ∞-norm based MPC cost, they are obtained as ∞-norm inequalities. It is shown that by using ∞-norms, the terminal constraint set is automatically obtained as a polyhedron or a finite union of polyhedra by taking a sublevel set of the calculated terminal cost function. New algorithms are developed for calculating polyhedral or piecewise polyhedral positively invariant sets for PWA systems. In this manner, the on-line optimization problem leads to a mixed integer quadratic programming problem or to a mixed integer linear programming problem, which can be solved by standard optimization tools. Several examples illustrate the effectiveness of the developed methodology
Modelling approaches for predictive control of large-scale sewage systems
In this report, model predictive control (MPC) of large-scale sewage systems is addressed considering different modelling approaches that include several inherent continuous/discrete phenomena
(overflows in sewers and tanks) and elements (weirs) in the system that result in distinct
behaviour depending on the dynamic state (
flow/volume) of the network. These behaviours
can not be neglected nor can be modelled by a pure linear representation. In order the MPC controller takes into account these phenomena and elements, a modelling approach based on piece-wise linear functions is proposed and compared against a hybrid modelling approach previously
reported by the authors. Control performance results and associated computation times
of the closed-loop scheme considering both modelling approaches are compared by using a real case study based on the Barcelona sewer network.Preprin
Approximate Explicit MPC and Closed-loop Stability: Analysis based on PWA Lyapunov Functions
Model Predictive Control (MPC) is the de facto standard in advanced industrial automation systems. There are two main formulations of the MPC algorithm: an implicit one and an explicit MPC one. The first requires an optimization problem to be solved on-line, which is the main limitation when dealing with hard real-time applications. As the implicit MPC algorithm cannot be guaran- teed in terms of execution time, in many applications the explicit MPC solution is preferable. In order to deal with systems integrating mixed logic and dynam- ics, the class of the hybrid and piecewise affine models (PWA) were introduced and tackled by the explicit MPC strategy. However, the resulting controller complexity leads to a requirement on the CPU/memory combination which is as strict as the number of states, inputs and outputs increases. To reduce drasti- cally the complexity of the explicit controller while preserving the controller’s performance, a strategy combining switched MPC with discontinuous simpli- cial PWA models is introduced in this thesis. The latter is proven to be circuit implementable, e.g., in FPGA. To ensure that closed-loop stability properties are guaranteed, a stability analysis tool is proposed which exploits suitable and possibly discontinuous PWA Lyapunov-like functions. The tool requires solving offline a linear programming problem. Moreover, the tool is able to compute an invariant set for the closed-loop system, as well as ultimate boundedness and input-to-state stability properties
Model predictive control techniques for hybrid systems
This paper describes the main issues encountered when applying model predictive control to hybrid processes. Hybrid model predictive control (HMPC) is a research field non-fully developed with many open challenges. The paper describes some of the techniques proposed by the research community to overcome the main problems encountered. Issues related to the stability and the solution of the optimization problem are also discussed. The paper ends by describing the results of a benchmark exercise in which several HMPC schemes were applied to a solar air conditioning plant.Ministerio de Eduación y Ciencia DPI2007-66718-C04-01Ministerio de Eduación y Ciencia DPI2008-0581
Approximate Dynamic Programming for Constrained Piecewise Affine Systems with Stability and Safety Guarantees
Infinite-horizon optimal control of constrained piecewise affine (PWA)
systems has been approximately addressed by hybrid model predictive control
(MPC), which, however, has computational limitations, both in offline design
and online implementation. In this paper, we consider an alternative approach
based on approximate dynamic programming (ADP), an important class of methods
in reinforcement learning. We accommodate non-convex union-of-polyhedra state
constraints and linear input constraints into ADP by designing PWA penalty
functions. PWA function approximation is used, which allows for a mixed-integer
encoding to implement ADP. The main advantage of the proposed ADP method is its
online computational efficiency. Particularly, we propose two control policies,
which lead to solving a smaller-scale mixed-integer linear program than
conventional hybrid MPC, or a single convex quadratic program, depending on
whether the policy is implicitly determined online or explicitly computed
offline. We characterize the stability and safety properties of the closed-loop
systems, as well as the sub-optimality of the proposed policies, by quantifying
the approximation errors of value functions and policies. We also develop an
offline mixed-integer linear programming-based method to certify the
reliability of the proposed method. Simulation results on an inverted pendulum
with elastic walls and on an adaptive cruise control problem validate the
control performance in terms of constraint satisfaction and CPU time
Fast Non-Parametric Learning to Accelerate Mixed-Integer Programming for Online Hybrid Model Predictive Control
Today's fast linear algebra and numerical optimization tools have pushed the
frontier of model predictive control (MPC) forward, to the efficient control of
highly nonlinear and hybrid systems. The field of hybrid MPC has demonstrated
that exact optimal control law can be computed, e.g., by mixed-integer
programming (MIP) under piecewise-affine (PWA) system models. Despite the
elegant theory, online solving hybrid MPC is still out of reach for many
applications. We aim to speed up MIP by combining geometric insights from
hybrid MPC, a simple-yet-effective learning algorithm, and MIP warm start
techniques. Following a line of work in approximate explicit MPC, the proposed
learning-control algorithm, LNMS, gains computational advantage over MIP at
little cost and is straightforward for practitioners to implement
Model Predictive Control for Signal Temporal Logic Specification
We present a mathematical programming-based method for model predictive
control of cyber-physical systems subject to signal temporal logic (STL)
specifications. We describe the use of STL to specify a wide range of
properties of these systems, including safety, response and bounded liveness.
For synthesis, we encode STL specifications as mixed integer-linear constraints
on the system variables in the optimization problem at each step of a receding
horizon control framework. We prove correctness of our algorithms, and present
experimental results for controller synthesis for building energy and climate
control
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