DSpace Repository :: Browsing by Author "Grancharova A."

Browsing by Author "Grancharova A."

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A Computational approach to explicit feedback stochastic nonlinear model predictive control
(2010-01-01) Grancharova A.; Johansen T.A.
Nonlinear Model Predictive Control (NMPC) involves the solution at each sampling instant of a finite horizon optimal control problem subject to nonlinear system dynamics, and state and input constraints. Mathematical models of engineering systems usually contain some amount of uncertainty. In the robust NMPC problem formulation, the model uncertainty is taken into account. This paper presents an approximate multi-parametric Nonlinear Programming approach to explicit solution of feedback stochastic MPC problems for constrained nonlinear systems in the presence of stochastic uncertainty. It is assumed that the discrete probability distribution of the uncertainty is known. The mathematical expectation of the cost function is minimized subject to state and input constraints. The approximate explicit approach constructs a piecewise nonlinear approximation to the optimal sequence of feedback control policies. It is demonstrated by explicit feedback stochastic NMPC for a cart moving on a plane and attached to the wall via a spring. ©2010 IEEE.
Approximate explicit constrained linear model predictive control via orthogonal search tree
(2003-05-01) Johansen T.; Grancharova A.
Solutions to constrained linear model predictive control problems can be precomputed offline in an explicit form as a piecewise linear state feedback on a polyhedral partition of the state-space, avoiding real-time optimization. We suggest an algorithm that will determine an approximate explicit piecewise linear state feedback by imposing an orthogonal search tree structure on the partition. This leads to a real-time computational complexity that is logarithmic in the number of regions in the partition, and the algorithm yields guarantees on the suboptimality, asymptotic stability and constraint fulfillment.
Approximate explicit model predictive control incorporating heuristics
(2002-01-01) Grancharova A.; Johansen T.
Explicit piecewise linear state feedback solutions to the constrained linear model predictive control problem have recently been characterized and computed numerically using multiparametric quadratic programming. The piecewise linear state feedback is defined on a polyhedral partitioning of the state space, which may be quite complex. Here we suggest an approximate multi-parametric quadratic programming approach, which has the advantages that the partition is structured as a binary search tree. This leads to real-time computation of the piecewise linear state feedback with a computational complexity that is logarithmic with respect to the number of regions in the partition. The algorithm is based on heuristic rules that are used to partition the state space and estimate the approximation error.
Computational aspects of approximate explicit nonlinear model predictive control
(2007-11-19) Grancharova A.; Johansen T.A.; Tøndel P.
It has recently been shown that the feedback solution to linear and quadratic constrained Model Predictive Control (MPC) problems has an explicit representation as a piecewise linear (PWL) state feedback. For nonlinear MPC the prospects of explicit solutions are even higher than for linear MPC, since the benefits of computational efficiency and verifiability are even more important. Preliminary studies on approximate explicit PWL solutions of convex nonlinear MPC problems, based on multi-parametric Nonlinear Programming (mp-NLP) ideas show that sub-optimal PWL controllers of practical complexity can indeed be computed off-line. However, for non-convex problems there is a need to investigate practical computational methods that not necessarily lead to guaranteed properties, but when combined with verification and analysis methods will give a practical tool for development and implementation of explicit NMPC. The present paper focuses on the development of such methods. As a case study, the application of the developed approaches to compressor surge control is considered. © 2007 Springer-Verlag Berlin Heidelberg.
Design of Explicit Model Predictive Controllers Based on Orthogonal Partition of the Parameter Space: Methods and A Software Tool
(2015-01-01) Grancharova A.
This paper reviews the approaches to explicit approximate Nonlinear Model Predictive Control (NMPC), based on orthogonal partition of the parameter space. They are classified with respect to the type of control problem, the type of model describing the nonlinear system, the presence of uncertainty, the type of control input, and the type of the approximating control function. A software tool for design of explicit NMPC by applying the described approaches is presented. It is used to design an explicit NMPC controller for a continuous stirred tank reactor.
Distributed Model Predictive Control of Time-Delay Systems
(2022-11-01) Grancharova A.; Olaru S.
In this paper, a new approach to distributed MPC of linear interconnected time-delay systems is proposed. The general case of time-delay in both the states and the control inputs is considered. The approach includes representation of the interconnected time-delay dynamics in the augmented state space and reformulation of the centralized MPC problem into a Quadratic Programming framework. The latter this is solved distributedly by using the dual gradient method for optimization. The suggested approach would be appropriate for embedded distributed MPC and is illustrated on a simulation example of two interconnected time-delay systems.
Distributed MPC-based path planning for UAVs under radio communication path loss constraints
(2012-01-01) Grancharova A.; Grøtli E.; Johansen T.
In this paper we address the Model Predictive Control (MPC)-based path planning problem for Unmanned Aerial Vehicles (UAVs). Our goal is to find trajectories that are safe with respect to grounding and collision, fuel efficient and satisfy criteria for communication such that the UAVs form a chain with a given radio communication capacity. A centralized MPC and a distributed MPC approaches to solve the path planning problem are proposed. Both approaches explicitly incorporate constraints on radio communication path losses, computed by using SPLAT!. In order to enhance the MPC problem computation, the terrain below each UAV and the communication path losses are approximated with linear functions. The control performance and the computational efficiency of the distributed MPC and the centralized MPC approaches are compared based on a simulation case study with two UAVs. © 2012 IFAC.
Distributed Nonlinear Model Predictive Control by Sequential Linearization and Accelerated Gradient Method
(2016-01-01) Grancharova A.; Johansen T.A.; Petrova V.
A suboptimal approach to distributed NMPC for nonlinear interconnected systems subject to constraints is proposed. The objective is to develop a computationally efficient approach. The suggested method is based on a sequential linearization of the nonlinear system dynamics and finding a suboptimal solution of the resulting Quadratic Programming problem by using distributed iterations of the dual accelerated gradient method. The benefits of the approach are reduced complexity of the on-line computations, and simple software implementation, which makes it appropriate for embedded distributed convex NMPC. The proposed method is illustrated with simulations on the model of a quadruple-tank system.
Distributed path planning for a UAV communication chain by dual decomposition
(2012-01-01) Grancharova A.; Grøtli E.; Johansen T.
In this paper, a distributed approach to Model Predictive Control (MPC)-based path planning for a UAV (Unmanned Aerial Vehicle) communication chain under radio path loss constraints is proposed. It is based on the dynamic dual decomposition method and reformulates the centralized path planning optimization problem with coupled constraints into an equivalent distributed path planning optimization problem, where the resulting sub-problems are completely decoupled. The MPC-based optimization sub-problems are computed autonomously within each UAV, using convex quadratic programming and gradient iterations, with the requirement that each UAV communicates its current measured position and the computed optimal velocity trajectory to its neighbouring UAVs. © 2012 IFAC.
Distributed predictive control based on Gaussian process models
(2023-03-01) Grancharova A.; Valkova I.; Hvala N.; Kocijan J.
A suboptimal approach to distributed NMPC is proposed based on Gaussian process models of the interconnected systems dynamics and taking into account the imposed constraints. The suggested method is based on a sequential linearization of the nonlinear system dynamics and finding a suboptimal solution of the resulting Quadratic Programming (QP) problem by using distributed iterations of the dual accelerated gradient method. The main advantages of the distributed approach are that it allows the computation of the suboptimal control inputs to be done autonomously by the subsystems without the need for centralized optimization and it has a simple software implementation. The proposed method is illustrated with simulations on the simplified model of a sewer system.
Distributed quasi-nonlinear model predictive control by dual decomposition
(2011-01-01) Grancharova A.; Johansen T.A.
A suboptimal approach to distributed NMPC for a class of systems consisting of nonlinear subsystems with linearly coupled dynamics subject to both state and input constraints is proposed. The approach applies a dual decomposition method to represent the original centralized NMPC problem into a distributed quasi-NMPC problem by linearization of the nonlinear system dynamics and taking into account the couplings between the subsystems. © 2011 IFAC.
Distributed Quasi-Nonlinear Model Predictive Control with Contractive Constraint
(2018-01-01) Grancharova A.; Johansen T.A.
An approach to low complexity distributed MPC of nonlinear interconnected systems with coupled dynamics subject to both state and input constraints is proposed. It is based on the idea of introducing a contractive constraint in the centralized NMPC problem formulation, which would guarantee the closed-loop system stability when using a small prediction horizon. Particularly, the one step ahead NMPC problem is considered. Further, a quasi-NMPC method is developed, which is based on a sequential linearization of the nonlinear system dynamics and finding distributedly a suboptimal solution of the resulting convex Quadratically Constrained Quadratic Programming problem. The suggested approach would be appropriate for distributed convex NMPC of some cyber-physical systems, since it will reduce the complexity of the on-line NMPC computations, simplify the software implementation, and reduce the requirements for available memory. The proposed method is illustrated with simulations on the model of a quadruple-tank system.
Dual-mode distributed Model Predictive Control of a quadruple-tank system
(2018-01-01) Grancharova A.; Johansen T.A.; Olaru S.
In this paper, a dual-mode distributed Model Predictive Control (MPC) approach is proposed in order to reduce the on-line computational complexity of the distributed optimal control of nonlinear interconnected systems. It consists in using a nonlinear distributed MPC approach when the state variables of the overall system are far from the origin and applying a linear distributed MPC method in a neighborhood of the origin. The nonlinear distributed approach is based on first-principles (nonlinear) models of the interconnected systems dynamics. It includes a sequential linearization of these models and finding distributedly a suboptimal solution of the resulting quadratic programming problem. In order to apply the linear distributed MPC method, it is necessary first to obtain a linearized model of the overall nonlinear system in a neighborhood of the origin. The benefit of the suggested dual-mode distributed MPC approach is the reduced complexity of the on-line computations in comparison to the entirely nonlinear approach when the current overall system state is in a neighborhood of the origin. The proposed method is illustrated with simulations on the model of a quadruple-tank system.
Explicit approaches to constrained model predictive control: A survey
(2004-01-01) Grancharova A.; Johansen T.A.
This paper presents a review of the explicit approaches to constrained model predictive control. The main motivation behind the explicit solution is that it avoids the need for real-time optimization, and thus allows implementation at high sampling frequencies in real-time systems with high reliability and low software complexity. The paper is organized as follows. Section 1 includes formulation of the constrained linear quadratic regulation (LQR) problem, summary of the implicit approaches, and the basics of the model predictive control (MPC). Sections 2 and 3 consider respectively the exact and the approximate approaches to explicit solution of constrained MPC problems, together with several examples.
Explicit approximate model predictive control of constrained nonlinear systems with quantized input
(2009-06-15) Grancharova A.; Johansen T.A.
In this paper, a Model Predictive Control problem for constrained nonlinear systems with quantized input is formulated and represented as a multi-parametric Nonlinear Integer Programming (mp-NIP) problem. Then, a computational method for explicit approximate solution of the resulting mp-NIP problem is suggested. The proposed approximate mp-NIP approach is applied to the design of an explicit approximate MPC controller for a clutch actuator with on/off valves. © 2009 Springer Berlin Heidelberg.
Explicit min-max model predictive control of constrained nonlinear systems with model uncertainty
(2005-01-01) Grancharova A.; Johansen T.A.
This paper presents an approximate multi-parametric nonlinear programming approach to explicit solution of constrained nonlinear model predictive control (MPC) problems in the presence of model uncertainty. The case of time-invariant parameter uncertainty is considered. The explicit MPC controller is based on an orthogonal search tree structure of the state space partition and is designed by solving a min-max optimization problem. It is robust in the sense that all constraints are satisfied for all possible values of the uncertain parameters. The approach is applied to design an explicit min-max MPC controller for a continuous stirred tank reactor, where the heat transfer coefficient is an uncertain parameter. Copyright © 2005 IFAC.
Explicit stochastic predictive control of combustion plants based on Gaussian process models
(2008-06-01) Grancharova A.; Kocijan J.; Johansen T.A.
Energy production is one of the largest sources of air pollution. A feasible method to reduce the harmful flue gases emissions and to increase the efficiency is to improve the control strategies of the existing thermoelectric power plants. This makes the Nonlinear Model Predictive Control (NMPC) method very suitable for achieving an efficient combustion control. Recently, an explicit approximate approach for stochastic NMPC based on a Gaussian process model was proposed. The benefits of an explicit solution, in addition to the efficient on-line computations, include also verifiability of the implementation, which is an essential issue in safety-critical applications. This paper considers the application of an explicit approximate approach for stochastic NMPC to the design of an explicit reference tracking NMPC controller for a combustion plant based on its Gaussian process model. The controller brings the air factor (respectively the concentration of oxygen in the flue gases) on its optimal value with every change of the load factor and thus an optimal operation of the combustion plant is achieved. © 2008 Elsevier Ltd. All rights reserved.
Fault tolerant predictive control for multi-agent dynamical systems: Formation reconfiguration using set-theoretic approach
(2014-12-23) Nguyen M.T.; Maniu C.S.; Olaru S.; Grancharova A.
This paper deals with the task assignment problem, which represents a major issue in dynamical formation control. The formation is defined in terms of a group of homogeneous dynamical agents. The position of each agent in the formation is predetermined by pre-imposing the distance between each pair of agents. Recently by using set-theoretic methods, the task assignment has been formulated in terms of an optimization problem allowing to keep the agents in a tight formation in real-time. In this paper we revisit these results and propose a new algorithm for the task assignment formulation in view of real-time control by including fault detection and isolation capabilities. The proposed methods will be illustrated by means of a numerical example.
Low Complexity Distributed Model Predictive Control by Using Contractive Sets
(2017-07-01) Grancharova A.; Olaru S.
In this paper, an approach to low complexity distributed MPC of linear interconnected systems with coupled dynamics subject to both state and input constraints is proposed. The suggested approach is based on the idea of introducing a contractive set constraint in the centralized MPC problem formulation, which would guarantee the closed-loop system stability when using a small prediction horizon. Then, a dual accelerated gradient method is applied to obtain distributedly a suboptimal solution of the resulting Quadratic Programming problem. The suggested approach would be appropriate for embedded distributed MPC since it will reduce the complexity of the on-line MPC computations, simplify the software implementation, and reduce the requirements for available memory.
Quantitative evaluation of alternatives for municipal solid waste treatment in Bulgaria
(2006-01-01) Grancharova A.; Boiadjiev D.; Lekova A.; Kostova S.
The present practice for treatment of municipal solid wastes in Bulgaria is to collect them in landfills. This leads to a serious ecological problem related to the emission of landfill gas which is extremely harmful for the environment (causing global warming). In this paper, four alternative policies for municipal waste treatment are defined (landfill without utilization of the landfill gas, landfill with producing synthetical gas from the landfill gas, landfill with producing electricity from the landfill gas and waste incineration with production of electricity). Four criteria to evaluate these alternatives are formulated. Selection of the best alternative is represented as a multi-criteria optimization problem and a strategy to solve this problem is developed. Copyright © 2006 IFAC.

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