Aircraft are dynamic systems that naturally contain a variety of constraints and nonlinearities such as, e.g., maximum permissible load factor, angle of attack and control surface deflections. Taking these limitations into account in the design of control systems are becoming increasingly important as the performance and complexity of the controlled systems is constantly increasing. It is especially important in the design of control systems for fighter aircraft. These 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 often maneuver the aircraft very close to the limit of what it is capable of, and an automatic system (called flight envelope protection system) against violating the restrictions is a necessity. In other application areas, nonlinear optimal control methods have been successfully used to solve this but in the aeronautical industry, these methods have not yet been established. One of the more popular methods that are well suited to handle constraints is Model Predictive Control (MPC) and it is used extensively in areas such as the process industry and the refinery industry. Model predictive control means in practice that the control system iteratively solves an advanced optimization problem based on a prediction of the aircraft's future movements in order to calculate the optimal control signal. The aircraft's operating limitations will then be constraints in the optimization problem. In this thesis, we explore model predictive control and derive two fast, low complexity algorithms, one for guaranteed stability and feasibility of nonlinear systems and one for reference tracking for linear systems. In reference tracking model predictive control for linear systems we build on the dual mode formulation of MPC and our goal is to make minimal changes to this framework, in order to develop a reference tracking algorithm with guaranteed stability and low complexity suitable for implementation in real time safety critical systems. To reduce the computational burden of nonlinear model predictive control several methods to approximate the nonlinear constraints have been proposed in the literature, many working in an ad hoc fashion, resulting in conservatism, or worse, inability to guarantee recursive feasibility. Also several methods work in an iterative manner which can be quit time consuming making them inappropriate for fast real time applications. In this thesis we propose a method to handle the nonlinear constraints, using a set of dynamically generated local inner polytopic approximations. The main benefits of the proposed method is that while computationally cheap it still can guarantee recursive feasibility and convergence. / <p>The series name "<em>Linköping studies in science and technology. Licentiate Thesis</em>" is incorrect. The correct series name is "<em>Linköping studies in science and technology. Thesis</em>".</p>

Indiana University-Purdue University Indianapolis (IUPUI) / This thesis studies critical zones of automated vehicles. The goal is for the automated vehicle to complete a car-following or lane change maneuver without collision. For instance, the automated vehicle should be able to indicate its interest in changing lanes and plan how the maneuver will occur by using model predictive control theory, in addition to the autonomous vehicle toolbox in Matlab. A test bench (that includes a scenario creator, motion logic and planner, sensors, and radars) is created and used to calculate the parameters of a critical zone. After a trajectory has been planned, the automated vehicle then attempts the car following or lane change while constantly ensuring its safety to continue on this path. If at any point, the lead vehicle brakes or a trailing vehicle accelerates, the automated vehicle makes the decision to either brake, accelerate, or abandon the lane change.

Magnetic Bearing Systems have been receiving a great deal of research attention for the past decades. Its inherent nonlinearity and open-loop instability are challenges for controller design. This thesis investigates and designs model predictive control strategy for an experimental Active Magnetic Bearing (AMB) laboratory system. A host-target development environment of real-time control system with hardware in the loop (HIL) is implemented. In this thesis, both continuous and discrete time model predictive controllers are studied. In the first stage, local MPC controllers are applied to control the AMB system; and in the second stage, concept of supervisory controller design is then investigated and implemented. Contributions of the thesis can be summarized as follows; 1. A Discrete time Model Predictive Controller has been developed and applied to the active magnetic bearing system. 2. A Continuous time Model Predictive Controller has been developed and applied to the active magnetic bearing system. 3. A frequency domain identification method using FSF has been applied to pursue model identification with respect to local MPC and magnetic bearing system. 4. A supervisory control strategy has been applied to pursue a two stages model predictive control of active magnetic bearing system.

An increasing number of applications ranging from multi-vehicle systems, large-scale process control systems, transportation systems to smart grids call for the development of cooperative control theory. Meanwhile, when designing the cooperative controller, the state and control constraints, ubiquitously existing in the physical system, have to be respected. Model predictive control (MPC) is one of a few techniques that can explicitly and systematically handle the state and control constraints. This dissertation studies the robust MPC and distributed MPC strategies, respectively. Specifically, the problems we investigate are: the robust MPC for linear or nonlinear systems, distributed MPC for constrained decoupled systems and distributed MPC for constrained nonlinear systems with coupled system dynamics. In the robust MPC controller design, three sub-problems are considered. Firstly, a computationally efficient multi-stage suboptimal MPC strategy is designed by exploiting the j-step admissible sets, where the j-step admissible set is the set of system states that can be steered to the maximum positively invariant set in j control steps. Secondly, for nonlinear systems with control constraints and external disturbances, a novel robust constrained MPC strategy is designed, where the cost function is in a non-squared form. Sufficient conditions for the recursive feasibility and robust stability are established, respectively. Finally, by exploiting the contracting dynamics of a certain type of nonlinear systems, a less conservative robust constrained MPC method is designed. Compared to robust MPC strategies based on Lipschitz continuity, the strategy employed has the following advantages: 1) it can tolerate larger disturbances; and 2) it is feasible for a larger prediction horizon and enlarges the feasible region accordingly. For the distributed MPC of constrained continuous-time nonlinear decoupled systems, the cooperation among each subsystems is realized by incorporating a coupling term in the cost function. To handle the effect of the disturbances, a robust control strategy is designed based on the two-layer invariant set. Provided that the initial state is feasible and the disturbance is bounded by a certain level, the recursive feasibility of the optimization is guaranteed by appropriately tuning the design parameters. Sufficient conditions are given ensuring that the states of each subsystem converge to the robust positively invariant set. Furthermore, a conceptually less conservative algorithm is proposed by exploiting the controllability set instead of the positively invariant set, which allows the adoption of a shorter prediction horizon and tolerates a larger disturbance level. For the distributed MPC of a large-scale system that consists of several dynamically coupled nonlinear systems with decoupled control constraints and disturbances, the dynamic couplings and the disturbances are accommodated through imposing new robustness constraints in the local optimizations. Relationships among, and design procedures for the parameters involved in the proposed distributed MPC are derived to guarantee the recursive feasibility and the robust stability of the overall system. It is shown that, for a given bound on the disturbances, the recursive feasibility is guaranteed if the sampling interval is properly chosen. / Graduate / 0548 / 0544 / 0546 / liuxiaotao1982@gmail.com

We review recent research into trajectory planning for autonomous overtaking to understand existing challenges. Then, the recently developed framework Learning Model Predictive Control (LMPC) is presented as a suitable method to iteratively improve an overtaking manoeuvre each time it is performed. We present recent extensions to the LMPC framework to make it applicable to overtaking. Furthermore, we also present two alternative modelling approaches with the intention of reducing computational complexity of the optimization problems solved by the controller. All proposed frameworks are built from scratch in Python3 and simulated for evaluation purposes. Optimization problems are modelled and solved using the Gurobi 9.0 Python API gurobipy. The results show that LMPC can be successfully applied to the overtaking problem, with improved performance at each iteration. However, the first proposed alternative modelling approach does not improve computational times as was the intention. The second one does but fails in other areas. / Vi går igenom ny forskning inom trajectory planning för autonom omkörning för att förstå de utmaningar som finns. Därefter föreslås ramverket Learning Model Predictive Control (LMPC) som en lämplig metod för att iterativt förbättra en omkörning vid varje utförande. Vi tar upp utvidgningar av LMPC-ramverket för att göra det applicerbart på omkörningsproblem. Dessutom presenterar vi också två alternativa modelleringar i syfte att minska optimeringsproblemens komplexitet. Alla tre angreppssätt har byggts från grunden i Python3 och simulerats i utvärderingssyfte. Optimeringsproblem har modellerats och lösts med programvaran Gurobi 9.0s python-API gurobipy. Resultaten visar att LMPC kan tillämpas framgångsrikt på omkörningsproblem, med förbättrat utförande vid varje iteration. Den första alternativa modelleringen minskar inte beräkningstiden vilket var dess syfte. Det gör däremot den andra alternativa modelleringen som dock fungerar sämre i andra avseenden.​

Model Predictive Control (MPC) refers to a class of algorithms that optimize the future behavior of the plant subject to operational constraints [46]. The merits of the class algorithms include its ability to handle imposed hard constraints on the system and perform on-line optimization. This thesis investigates design and implementation of continuous time model predictive control using Laguerre polynomials and extends the design ap- proaches proposed in [43] to include intermittent predictive control, as well as to include the case of the nonlinear predictive control. In the Intermittent Predictive Control, the Laguerre functions are used to describe the control trajectories between two sample points to save the com- putational time and make the implementation feasible in the situation of the fast sampling of a dynamic system. In the nonlinear predictive control, the Laguerre polynomials are used to describe the trajectories of the nonlinear control signals so that the reced- ing horizon control principle are applied in the design with respect to the nonlinear system constraints. In addition, the thesis reviews several Quadratic Programming methods and compares their performances in the implementation of the predictive control. The thesis also presents simulation results of predictive control of the autonomous underwater vehicle and the water tank.

Repetitive Model Predictive Control (RMPC) incorporates the idea of Repetitive Control (RC) into Model Predictive Control (MPC) to take full advantage of the constraint handling, multivariable control features of MPC in periodic processes. The RMPC achieves perfect asymptotic tracking/rejection in periodic processes, provided that the period length used in the control formulation matches the actual period of the reference/disturbance exactly. Even a small mismatch between the actual period of process and the controller period can deteriorate the RMPC performance significantly. The period mismatch occurs either from an inaccurate estimation of actual frequency of disturbance due to resolution limit or from trying to force the controller period to be an integer multiple of sampling time. An extension of RMPC called Robust Repetitive Model Predictive Control (R-RMPC) is proposed for such cases where period length cannot be predetermined accurately, or where period is not an integer multiple of sampling time. This robust RMPC borrows the idea of using weighted, multiple memory loops in RC for robustness enhancement. The modified RMPC is more robust in the sense that small changes in period length do not diminish the tracking/rejection properties by much. Simulation results show that R-RMPC achieves significant improvement over the standard RMPC in case of a slight period mismatch. The effectiveness of this Robust RMPC is demonstrated by applying it to a mechanical motion tracking machine whose function is to follow a constant trajectory while rejecting periodic disturbances of an uncertain period.

Motivated by the goal of transition to a zero-carbon-emission-based economy for climate change mitigation, electrification opportunities are more promising in the transportation sector. Electric Vehicles (EVs) are at the forefront of the energy transition at an expanded rapid pace in the transportation sector. To enable and enhance the energy efficiency, advanced control and optimization will play an important role in EV systems and infrastructure. However, there are also some difficulties and limitations subject to the imperfection of management and control for EVs. Overall, to further the widespread adoption of EVs, the dissertation mainly includes two parts: 1) Power management for Plug-in Hybrid Electric Vehicles (PHEVs); 2) Charging control for Plug-in Electric Vehicles (PEVs). Chapter 2 deals with the power management and route planning problems for PHEVs, which aims to properly design the control algorithm to find the route that leads to the minimum energy consumption. Chapter 3 pays attention to the high workloads of the PEV in the electric power grids, which concentrates on studying a control algorithm leading to possible reductions in both computation and communication. Chapter 4 focuses on the charging control for PEVs, which explores how to improve the PEV charging efficiency while satisfying safety concerns. Chapter 5 modifies the results in Chapter 4 by taking battery capacity degradation into the optimization problem. This dissertation proceeds with Chapter 1 by reviewing the state-of-the-art control methods for PEVs and PHEVs. Chapter 2 studies a novel control scheme of route planning with power management for PHEVs. By considering the power management of PHEVs, we aim to find the route that leads to the minimum energy consumption. The scheme adopts a two-loop structure to achieve the control objective. Specifically, in the outer loop, the minimum energy consumption route is obtained by minimizing the difference between the value function of current round and the best value from all previous rounds. In the inner loop, the energy consumption index with respect to PHEV power management for each feasible route is trained with Reinforcement Learning (RL). Under the RL framework, a nonlinear approximator structure, which consists of an actor approximator and a critic approximator, is built to approximate control actions and energy consumption. In addition, the convergence of value function for PHEV power management in the inner loop and asymptotical stability of the closed-loop system are rigorously guaranteed. Chapter 3 investigates the self-triggered Model Predictive Control (MPC) with Integral Sliding Mode (ISM) method of a networked nonlinear continuous-time system subject to state and input constraints with additive disturbances and uncertainties. Compared with the standard MPC strategy, the proposed control scheme is designed for PEV charging to reduce the high communication loads caused by a large-scale population of vehicles under centralized charging control architecture. In the proposed scheme, the constrained optimization problem is solved aperiodically to generate control signals and the next execution time, leading to possible reductions in both computation and communication. The motivation of using ISM approach is to reject matched uncertainties. A self-triggered condition that involves a comparison between the cost function values with different execution periods is derived. Besides, the robust MPC with ISM control strategy is rigorously studied depending on the self-triggered scheme. Chapter 4 proposes a charging control algorithm for the valley-filling problem, while it meets individual charging requirements. We study a decentralized framework of PEV charging problem with a coordination task. An iterative learning-based model predictive charging control algorithm is developed to achieve the valley-filling performance. The design of the decentralized MPC meets individual charging requirements. The iterative learning method approximates the electricity price function and the system state sampled safe set to improve the accuracy of optimization problem calculations. The decentralized problem, in which the individual PEV minimizes its own charging cost, is formulated based on the sum of all power loads. Chapter 5 studies a modified charging control algorithm based on the previous charging control algorithm in Chapter 4. We propose a charging control algorithm for PEVs using a decentralized MPC framework supplemented by the iterative learning method. By considering the battery aging of PEVs, we aim to find the optimal charging rate that leads to valley-filling performance. The scheme adopts the iterative learning-based method to solve the optimal control problem with the battery aging model. Specifically, the sampled safe set and price function are updated accordingly as the iteration number increases. The battery aging model involves the cost function to approach the real charging scenario. In addition, the recursive feasibility of the proposed optimal control problem for PEV charging with battery aging and asymptotical stability of the closed-loop system are rigorously studied. Finally, in Chapter 6, the conclusions of the dissertation and some avenues for future potential research are presented. / Graduate / 2023-04-07

Accidental collisions involving wheeled industrial ground vehicles can be costly to repair, cause serious (even fatal) human injury, and lead to setbacks with tight operation schedules. Reduction of vehicle collisions carries numerous safety and financial incentives. In this work, an integrated collision avoidance package is developed to reduce the number of vehicle collisions. Utilizing feedback from on-board sensing devices, a model predictive control (MPC) algorithm predicts control options and paths, then disallows drivers to accelerate and/or induces braking of the vehicle if a collision is imminent. A prototype system is developed, implemented, and tested on an industrial vehicle to mitigate collisions with people and high-value equipment. Testing results show that control can be executed in real time by the proposed system, and that the proposed method is effective in preventing an industrial vehicle from hitting detected obstacles and entering restricted areas.

<p>Model Predictive Control (MPC) is traditionally designed assuming no model mismatch and tuned to provide acceptable behavior when mismatch occurs. This thesis extends the MPC design to account for explicit mismatch in the control and optimization of a wide range of uncertain dynamic systems with feedback, such as in process control and supply chain optimization.</p> <p>The major contribution of the thesis is the development of a new MPC method for robust performance, which offers a general framework to optimize the uncertain system behavior in the closed-loop subject to hard bounds on manipulated variables and soft bounds on controlled variables. This framework includes the explicit handling of correlated, time-varying or time-invariant, parametric uncertainty appearing externally (in demands and disturbances) and internally (in plant/model mismatch) to the control system. In addition, the uncertainty in state estimation is accounted for in the controller.</p> <p> For efficient and reliable real-time solution, the bilevel stochastic optimization formulation of the robust MPC method is approximated by a limited number of (convex) Second Order Cone Programming (SOCP) problems with an industry-proven heuristic and the classical chance-constrained programming technique. A closed-loop uncertainty characterization method is also developed which improves real-time tractability by performing intensive calculations off-line.</p> <p>The new robust MPC method is extended for process control problems by integrating a robust steady-state optimization method addressing closed-loop uncertainty. In addition, the objective function for trajectory optimization can be formulated as nominal or expected dynamic performance. Finally, the method is formulated in deviation variables to correctly estimate time-invariant uncertainty.</p> <p>The new robust MPC method is also tailored for supply chain optimization, which is demonstrated through a typical industrial supply chain optimization problem. The robust MPC optimizes scenario-specific safety stock levels while satisfying customer demands for time-varying systems with uncertainty in demand, manufacturing and transportation. Complexity analysis and computational study results demonstrate that the robust MPC solution times increase with system scale moderately, and the method does not suffer from the curse of dimensionality.</p> / Thesis / Doctor of Philosophy (PhD)