Robust feedback model predictive control of norm-bounded uncertain systems

This thesis is concerned with the Robust Model Predictive Control (RMPC) of linear discrete-time systems subject to norm-bounded model-uncertainty, additive disturbances and hard constraints on the input and state. The aim is to design tractable, feedback RMPC algorithms that are based on linear matrix inequality (LMI) optimizations. The notion of feedback is very important in the RMPC control parameterization since it enables effective disturbance/uncertainty rejection and robust constraint satisfaction. However, treating the state-feedback gain as an optimization variable leads to non-convexity and nonlinearity in the RMPC scheme for norm-bounded uncertain systems. To address this problem, we propose three distinct state-feedback RMPC algorithms which are all based on (convex) LMI optimizations. In the first scheme, the aforementioned non-convexity is avoided by adopting a sequential approach based on the principles of Dynamic Programming. In particular, the feedback RMPC controller minimizes an upper-bound on the cost-to-go at each prediction step and incorporates the state/input constraints in a non-conservative manner. In the second RMPC algorithm, new results, based on slack variables, are proposed which help to obtain convexity at the expense of only minor conservatism. In the third and final approach, convexity is achieved by re-parameterizing, online, the norm-bounded uncertainty as a polytopic (additive) disturbance. All three RMPC schemes drive the uncertain-system state to a terminal invariant set which helps to establish Lyapunov stability and recursive feasibility. Low-complexity robust control invariant (LC-RCI) sets, when used as target sets, yield computational advantages for the associated RMPC schemes. A convex algorithm for the simultaneous computation of LC-RCI sets and the corresponding controller for norm-bounded uncertain systems is also presented. In this regard, two novel results to separate bilinear terms without conservatism are proposed. The results being general in nature also have application in other control areas. The computed LC-RCI sets are shown to have substantially improved volume as compared to other schemes in the literature. Finally, an output-feedback RMPC algorithm is also derived for norm-bounded uncertain systems. The proposed formulation uses a moving window of the past input/output data to generate (tight) bounds on the current state. These bounds are then used to compute an output-feedback RMPC control law using LMI optimizations. An output-feedback LC-RCI set is also designed, and serves as the terminal set in the algorithm.Open Acces

Cascaded Control for Improved Building HVAC Performance

As of 2011 buildings consumed 41% of all primary energy in the U.S. and can represent more than 70% of peak demand on the electrical grid. Usage by this sector has grown almost 50% since the 1980s and projections foresee an additional growth of 17% by 2035 due to increases in population, new home construction, and commercial development. Three-quarters of building energy is derived from fossil fuels making it a large contributor of the country’s CO2 and NOx output both of which greatly affect the environment and local air quality. Up to half of energy used by the building sector is related to Heating, Ventilation, and Air-Condition systems. Focusing on improving building HVAC control therefore has a large aggregate effect on US energy usage with economic and environmental benefits for end users. This dissertation develops cascaded loop architectures as a solution to common HVAC control issues. These systems display strong load-dependent nonlinearities and coupling behaviors that can lead to actuator hunting (sustained input oscillations) from standard PI controllers that waste energy and cost money. Cascaded loops offer a simple way to eliminate hunting and decouple complex HVAC systems with minimal a priori knowledge of system dynamics. As cascaded loops are easily implementable in building automation systems they can be readily and widely adopted in the field. An examination of the current state of PI control in HVAC and discussion of coordinated, optimal control strategies being developed for reduced energy usage are discussed in Chapter 1. The following two chapters outline the structure and benefits of the cascaded architecture and demonstrate the same using a series of simulation case studies. Implementation approaches and parameterizations of the architecture are explored in Chapter 4 with a derivation showing that the addition of an additional feedback path (i.e., inner loop control) provides more design freedom and ultimately allows for improved control. Finally, Chapter 5 details results from initial cascaded loop implementation at three campus buildings. Results showed improved control performance and an elimination of identified hunting behavior

Optimal network implementable controllers for networked systems

In this thesis, we study the problem of network implementable controllers for network distributed systems. Network distributed control problem gains importance by the increase in networked system applications in many areas which require network distributed control and estimation. By network implementable controller, we mean controller can be implemented over the given network with the predefined/given delay and sparsity constraints. We define all stabilizing controllers by re-interpreting plant and controller. We define a congruent stable plant of the original plant which is not necessarily stable, such that the controller of the congruent plant is linearly function of the original plant\u27s controller. When we put structural constraints on all stabilizing controllers of the stable congruent plant, these controllers embody controllers of the main plant. Therefore, all stabilizing controllers of the original plant are defined as all stabilizing controllers of the congruent plant with structural constraints. In the view of this problem, we obtain all stabilizing controller parametrization of the original plant wherein equality constraints are introduced on the Youla parameter. Moreover, we define a necessary and sufficient problem to attain a controller in the form of norm minimization problem benefiting formulated all stabilizing controller parametrization and provide a solution method for it. Moreover, we introduce a doubly-coprime factorization of blkdiag(I_{n_x}, K) which allows us to have a network implementable state-space realization of a structured controller, K, which inherits sparsity and delay constraints introduced by the given network in z-domain, of a network distributed system with order n_x. By network implementable state-space realization, we mean state-space realization can be expressed as a strictly causal interaction of some sub-systems over the given network. We call such structured controllers as network realizable controller, i.e. controllers whose network implementable state-space realization can be obtained. Moreover, using the formulated controller problem, we provide a network realizable controller problem by introducing sparsity and delay constraints on the Youla parameter. Introduced network realizable controller problem is in the form of norm minimization problem with structural constraints introduced on Youla parameter. Afterwards, we obtain its equivalent unconstrained network realizable controller problem which allows us to attain a solution in infinite dimensional space benefiting existing solution methods of H_2 problem. Moreover, we define a model matching problem and present an optimal network realizable controller problem. The formulated optimal network realizable controller problem is a constrained problem. To obtain an unconstrained problem formulation, we define a relaxation by a Lagrange multiplier and benefit from the vectorization method introduced in the literature. Formulated unconstrained problem allows us to obtain a solution using existing solution methods wherein solution lies in infinite dimensional space. Once the optimal network realizable controller is obtained, we obtain a network implementable state-space realization of it using the method we have introduced. Furthermore, we provide an alternative all stabilizing network realizable controller \linebreak parametrization benefiting existing Youla parametrization which requires to have an initial controller. We show that when the given initial controller is network realizable, one can parametrize all stabilizing network realizable controllers with a network realizable Youla parameter. Moreover, we introduce network realizable controllers in the form of delayed controllers for strongly connected networked plants which allow us to parametrize all stabilizing network realizable controllers with the Youla parametrization aforementioned. We derive a model matching problem and define a necessary and sufficient optimal network realizable controller problem as a function of initial network realizable controller with sparsity and delay constraints introduced on Youla parameter. Moreover, we provide its equivalent unconstrained problem benefiting vectorization method wherein a solution in infinite dimensional space can be obtained benefiting existing solution methods