A Distributionally Robust Optimization Model for Vehicle Platooning Under Stochastic Disturbances

The synergy between optimization and control is a long standing tradition. In fact, this synergy is becoming more and more apparent because of the multi-disciplinary character of the most pressing, current engineering problems along with constant developments of these two fields. Historically, optimization methods have helped the control community to achieve their design goals formalized in some sort of objective function. On the other hand, control theory has provided a setting to interpret complicated aspects of optimization algorithms. In this thesis, we address three problem instances that lie on the boundary of optimization and control. We employ tools from one field to address a problem in the other field. Fundamentally, our proposed methods share a similar character: their analysis techniques are trajectory-based. In simple words, our proposed methods exploit the trajectories generated by the dynamics that represent each problem instance. The first problem focuses on a 2nd-order, damped differential equation (ODE). This ODE along with its numerous variations have been used to develop or analyze various optimization algorithms, known as fast methods. As an alternative to the existing methods, we first amend the underling ODE with two types of state-dependent inputs, and then extend the resulting controlled dynamics to two hybrid control systems. Employing a trajectory-based analysis, both control laws are constructed to guarantee exponential convergence in a suboptimality measure. To show that the trajectories generated by each hybrid control system are well-posed, we demonstrate Zeno-freeness of solution trajectories in both cases. Furthermore, we propose a mechanism to determine a time-discretization step-size such that the resulting discrete-time hybrid control systems are exponentially stable. Event-based implementation of control laws have received a lot of attention during the past decade. The reason for this interest is the hope to reduce the conservatism involved in the traditional periodic implementation. In the second problem of this thesis, we introduce an event-based sampling policy for a constraint-tightening, robust model predictive control (RMPC) method. The triggering mechanism is a sequence of hyper-rectangles constructed around the optimal state trajectories. In particular, the triggering mechanism's nature makes the proposed approach a suitable choice for plants without a centralized sensory node. A key feature of the proposed method is its complete decoupling from the RMPC method's parameters, facilitating a meaningful comparison between the periodic and aperiodic implementation policies. Furthermore, we provide two types of convex formulations to design the triggering mechanism. The last problem we focus on in this thesis is also related to the event-based implementation of a control law. However, the main aim here is to propose an entity that can be utilized by a real-time engineer to schedule tasks in a networked structure. A common entity provided in the literature related to event-triggering approaches is the minimal inter-execution time (to show the avoidance of a Zeno behavior in the closed-loop system). Nonetheless, such a quantity is extremely conservative when used for scheduling purposes. In this problem, we consider an $\mathcal{L}_2$-based triggering mechanism introduced in the literature and propose a framework to construct a timed safety automaton that can capture the triggering instants generated by this mechanism. In our analysis, we borrow some tools from stability analysis of delayed systems along with reachability analysis to construct the desired timed safety automaton.

The model predictive control method can be effective for converter control in distributed power generation but requires a large amount of computation, leading to a considerable time delay in the actuation. If the delay is not reflected, the system performance could get worse. This paper presents a two-step (horizon) prediction algorithm of model predictive control technique for grid-tied inverters used in wind turbine systems. The control objectives such as active and reactive power flow and switching loss reduction are reflected in the objective function of the controller. The proposed model predictive control strategy is verified numerically by using MATLAB/Simulink.

Recent developments in vehicle onboard computers and vehicle-to-vehicle communications technology allow automatic control of vehicles and the organization of vehicles into platoons with short intraplatoon distances. One of the major issues with platoon control is latency in wireless communications. Latency has a negative impact on safety and disrupts the stability of platoons. A decentralized longitudinal platoon-controlling mechanism that uses a model predictive control approach to control vehicles safely, even in harsh communications environments, is proposed. The sensitivity of this method was analyzed to derive the conditions for this method to work safely. A simulation test bed for this control method was implemented to test effectiveness and safety under two communications latency settings. The results showed that the model predictive control method could safely control the platoon even in harsh communications environments.

For the input and output constraints and uncertainties in batch processes, a 2D output feedback robust constrained model predictive control (MPC) method is designed by combining iterative learning control (ILC), MPC and output feedback. Firstly, an equivalent 2D-FM closed-loop prediction model is established by combining with the proposed output feedback controller. Then an optimization performance index function with terminal constraint is constructed to study its control optimization. According to the designed optimization performance index and Lyapunov stability theory, the feasible MPC problem is obtained by solving the linear matrix inequalities (LMIs). At the same time, the gain of the new output feedback control law is given to ensure that the performance index reaches the minimum upper bound under the constraints of input and output. In order to solve the manual adjustment problem of some parameters in the performance index function, the particle swarm optimization (PSO) algorithm is introduced, and a better solution is found near the controller by using the search optimization method. Finally, taking the injection molding process as an example and comparing with the existing method without using PSO algorithms, it is proved that the above method is more feasible.

A novel power and rate control system model for wireless communication networks is presented, which includes uncertainties, input constraints, and time-varying delays in both state and control input. A robust delay-dependent model predictive power and rate control method is proposed, and the state feedback control law is obtained by solving an optimization problem that is derived by using linear matrix inequality (LMI) techniques. Simulation results are given to illustrate the effectiveness of the proposed method.

This paper presents an on–line image based visual servoing (IBVS) controller for a 6 DOF robotic system based on the robust model predictive control (RMPC) method. The controller is designed considering the robotic visual servoing system’s input and output constraints, such as robot physical limitations and visibility constraints. The proposed IBVS controller avoids the inverse of the image Jacobian matrix and hence can solve the intractable problems for the classical IBVS controller, such as large displacements between the initial and the desired positions of the camera. To verify the effectiveness of the proposed algorithm, real–time experimental results on a 6 Degrees–of–Freedom (DOF) robot manipulator with eye–in–hand configuration are presented

This study presents a novel robust model predictive control (MPC) method for constrained non-linear systems with control constraints and external disturbances. The control signal is obtained by optimising an objective function consisting of two terms: an integral non-squared stage cost and a non-squared terminal cost. The terminal weighting matrix is designed appropriately such that: (i) the terminal cost serves as a control Lyapunov function; and (ii) the resultant finite horizon cost can be treated as a quasi-infinite horizon cost. Provided that the Jacobian linearisation of the system to be controlled is stabilisable and the optimisation is initially feasible, sufficient conditions ensuring the recursive feasibility of the optimisation and the robust stability of the closed-loop system are established. It is shown that the conditions rely on an appropriate design of the sampling interval with respect to a certain given disturbance level. The effectiveness of the proposed method is illustrated through a numerical example.

This paper proposes a model predictive controller for two-stage inverter with less switching losses and capacitor current. In implementation, model predictive control (MPC) method is simple and flexible without assuming the traditional PWM block. As the capacitor current has great influence on the capacitor losses and lifetime, an adjustment before the switching signals are sent to the switches is added in the proposed MPC method to reduce the capacitor current RMS value. The decrease of capacitor current RMS value enables the reduction of capacitor losses and the increase of capacitor lifetime. Besides, the proposed method can achieve less switching losses of front-end dc-dc converter, compared with the conventional MPC method. This paper presents the detailed operational principle of proposed MPC method and compares the performance of conventional and proposed MPC methods using the same system parameters. Finally, the simulation and experimental results verified the validity and advantage of the proposed method.

This paper presents centralized control for a wind farm using model predictive control (MPC) method. In order to solve intra-day unit commitment (UC) problem, the UC problem is solved by using the MPC method with short-term wind power forecasting. We introduce a new dynamics model for the UC with some constraints to utilize the benefits of the MPC method. The objective function considering the operation and maintenance costs is formulated by adding a new variable in order to average the operating time of each wind turbine (WT) within the whole time. The proposed method could solve the UC problems on-line using the prediction time horizon that could be selected flexibly considering time horizon based on wind power forecasting errors. From the simulation study using 10 WTs, we observed that the proposed dynamics model of UC effectively provided the optimal solution to each scenario. Numerical study will validate that the proposed method can be applied to solving the UC problem of a large scale wind farm by aggregating WTs.

A stochastic model predictive control (SMPC) method is proposed for trajectory tracking of quadrotor helicopters with stochastic disturbances. The stochastic disturbances are assumed to be Gaussian white noises. The existing robust control methods generally guarantee that the tracking performances under the worst-case disturbances satisfying given conditions. However, the worst-case disturbances may have a vanishingly small probability of occurrence in practice, so these methods show great conservative. In this paper, the tracking errors caused by the disturbances are limited in the acceptable range with the given probability. The hierarchical control structure is used. In the outer loop, the position loop, SMPC controllers are designed for position tracking. In the inner loop, the attitude loop, the nonlinear dynamics are linearized by the feedback linearization strategy, and an SMPC controller is designed for attitude tracking. Finally, simulation results verify the effectiveness of the proposed method.

Traffic congestion has become a significant issue in urban road networks. There have been massive works about traffic signal optimization to improve the efficiency of traffic flow operation, and the so-called back-pressure control policy has proven to be excellent for oversaturated conditions. Most of the existing works with back-pressure are based on an adaptive phase sequence, and research with cyclic phase sequence is based on calculating the splits for different phases using the traffic flow data at the beginning of each cycle, which is unfair for the non-initial phases. In this paper, we propose a decentralized model predictive signal control method with fixed phase sequence using back-pressure policy. The main idea of the new method is to form a control loop using the model predictive control, enabling the system to obtain real-time feedback from the traffic network and dynamically adjusting signal timing plans at the beginning of each phase. As links within a certain area have various lengths, the same queue length can imply different traffic conditions, so a method to normalize queue lengths is proposed. The normalized queue length decreases drastically when the actual length approaches link capacity, thus avoiding spillover. The proposed method was tested in a virtual road network. Numerical results suggest that the new method improves performance under congested conditions in terms of throughput, Gini coefficient and comprehensive transportation efficiency.

Chapter 8 - Event-triggered resilient platoon control: Distributed dynamic event-triggered secure model predictive control of vehicle platoon against DoS attacks

To improve the load frequency control (LFC) performance of power systems incorporating virtual power plants (VPPs) while reducing network resource consumption, a model predictive control (MPC) method based on a mixed time/event-triggered mechanism (MTETM) is proposed. This mechanism integrates an event-triggered mechanism (ETM) with a time-triggered mechanism (TTM), where ETM avoids unnecessary signal transmission and TTM ensures fundamental control performance. Subsequently, for the LFC system incorporating VPPs, a state hard constrained MPC problem is formulated and transformed into a “min-max” optimisation problem. Through linear matrix inequalities, the original optimisation problem is equivalently transformed into an auxiliary optimisation problem, with the optimal control law solved via rolling optimisation. Theoretical analysis demonstrates that the proposed auxiliary optimisation problem possesses recursive feasibility, whilst the closed-loop system satisfies input-to-state stability. Finally, validation through case studies of two regional power systems demonstrates that the MPC approach based on MTETM outperforms the ETM-based MPC approach in terms of control performance while maintaining a triggering rate of 33.3%. Compared with the TTM-based MPC algorithm, the MTETM-based MPC method reduces the triggering rate by 66.7%, while maintaining nearly equivalent control performance. Consequently, the results validate the effectiveness of the MTETM-based MPC approach in conserving network resources while maintaining control performance.

This paper proposes a time-lag model predictive control (MPC) method to solve the problem of communication delay in networked automatic generation control (AGC). The method uses the optimum weighting method to predict delay and the time-lag dynamic state equation of interconnected grid as the MPC prediction model. Then the deviation of predicted output is added to the objective function of rolling optimization in MPC method. The backup suboptimal control command from MPC controller can handle the loss of data packet in networked AGC. The correctness of the proposed method is verified by dynamic simulation.

This paper proposes a highly efficient single-phase three-level neutral point clamped (NPC) converter operated by a model predictive control (MPC) method with reduced commutations of switches. The proposed method only allows switching states with none or a single commutation at the next step as candidates for future switching states for the MPC method. Because the proposed method preselects switching states with reduced commutations when selecting an optimal state at a future step, the proposed method can reduce the number of switchings and the corresponding switching losses. Although the proposed method slightly increases the peak-to-peak variations of the two dc capacitor voltages, the developed method does not deteriorate the input current quality and input power factor despite the reduced number of switching numbers and losses. Thus, the proposed method can reduce the number of switching losses and lead to high efficiency, in comparison with the conventional MPC method.