In this work, we consider the control of discrete-time constrained nonlinear systems over unreliable packet-based communication networks. The random packet-dropouts are modeled by a two-state Markov chain and no acknowledgments of receipt are assumed. In order to weaken the impact of the packet dropouts, the controller transmits packets containing more than one future control input and a suitable buffering is applied at the plant actuator side. Since the Markov chain model adopted does not ensure the number of consecutive packet dropouts to be bounded, deterministic stability cannot be guaranteed. Hence, we are interested in stochastic stability of the closed-loop instead. We propose an unconstrained model predictive control (MPC) scheme without additional terminal weighting term for the calculation of the control inputs. Two major advantages of this unconstrained MPC scheme can be emphasized. First, in order to guarantee stochastic stability we do not require the knowledge of a global control Lyapunov function as terminal cost term, but instead only a less restrictive controllability assumption. Second, guaranteed performance bounds on the expected infinite horizon cost of the closed-loop can be obtained.

This paper presents a continuous-time version of recent results on unconstrained nonlinear model predictive control (MPC) schemes. Based on a controllability assumption and a corresponding infinite-dimensional optimization problem, performance estimates and stability conditions are derived in terms of the prediction horizon and the sampling time of the MPC controller. Moreover, improved estimates for small sampling times are discussed and a comparison to the application of the discrete-time results in a sampled-data context is provided.

In this paper, we propose a general framework for distributed model predictive control of discrete-time nonlinear systems with decoupled dynamics but subject to coupled constraints and a common cooperative task. To ensure recursive feasibility and convergence to the desired cooperative goal, the systems optimize a local cost function in a sequential order, whereas only neighbor-to-neighbor communication is allowed. In contrast to most of the existing distributed model predictive control schemes in the literature, we do not necessarily consider the stabilization of an a priori known set point. Instead, also other cooperative control tasks such as consensus and synchronization problems can be handled within the proposed framework. In particular, one of our main contributions is to show how for the latter case the terminal cost functions and the terminal region can be suitably defined and computed. Furthermore, we illustrate our results with simulation examples.

In this work, we present results on model predictive control (MPC) for nonlinear time-delay systems. MPC is one of the few control methods which can deal effectively with constrained nonlinear time-delay systems. In order to guarantee stability of the closed-loop, a local control Lyapunov functional in a region around the origin is in general utilized as terminal cost. It is well-known for delayfree systems that a control Lyapunov function calculated for the Jacobi linearization about the origin can also be used as a terminal cost for the nonlinear system for an appropriately chosen terminal region. However, the infinite-dimensional nature of time-delay systems circumvents a straight-forward extension of those schemes to time-delay systems. We present two schemes for calculating stabilizing design parameters based on the Jacobi linearization of the nonlinear time-delay system. The two schemes are based on different assumptions and yield different types of terminal regions. We compare the properties and discuss advantages and disadvantages of both schemes.

This paper proposes a model predictive control scheme for non-linear time-delay systems with input constraints. Based on the results for systems without delays, asymptotic stability of the closed loop is guaranteed by utilizing an appropriate terminal cost functional and an appropriate terminal region such that the optimal cost for the finite-horizon problem is an upper bound on the optimal cost for the associated infinite-horizon problem. Two structured procedures are presented to determine offline the terminal cost and the terminal region for a class of non-linear time-delay systems. For both procedures, sufficient conditions can be formulated in terms of linear matrix inequalities based on the Jacobi linearization of the system about the origin. The first procedure uses a combination of Lyapunov-Krasovskii and Lyapunov-Razumikhin conditions in order to compute a locally stabilizing controller and a control invariant region. The second procedure only applies Lyapunov-Krasovskii arguments but may yield more complicated control invariant regions. The effectiveness of both schemes is compared for the example of a continuous stirred tank reactor with recycle stream.

This paper presents a new model predictive control (MPC) scheme for linear constrained discrete-time periodic systems. In each period of the system, a new periodic state feedback control law is computed via a convex optimization problem that minimizes an upper bound of an infinite horizon cost function subject to state and input constraints. The performance of the proposed model predictive controller, that stabilizes the discrete-time periodic system if it is initially feasible, is illustrated via an example.

In this work, we present two unconstrained MPC schemes using additional weighting terms which allow to obtain improved stability conditions. First, we consider unconstrained MPC with general terminal cost functions. If the terminal cost is not a control Lyapunov function, but satisfies a relaxed condition, then our results yield improved estimates for a stabilizing prediction horizon. Furthermore, our analysis also allows to recover two well-known results as special cases: if the terminal cost function is chosen as zero, we recover previous conditions on the length of the prediction horizon such that stability is guaranteed; and if the terminal cost is a control Lyapunov function conform to the stage cost, stability follows independently of the length of the prediction horizon. Second, we propose to use an exponential weighting on the stage cost in order to improve the stability properties of the closed-loop. This also allows to consider local controllability assumptions in combination with a suitable terminal constraints and thereby gives a connection to the classical MPC approaches using terminal constraints.

This work presents a novel model predictive control (MPC) scheme using a generalized integral terminal cost term. This generalized scheme exhibits close connections to recent results on unconstrained MPC as well as classical MPC using control Lyapunov functions as terminal weights. In particular, we show that both previous results can be regarded as limit cases of our setup. An example illustrates possible advantages provided by the increased flexibility of the proposed scheme compared to the previous results.

In this work, we consider the control of discrete-time nonlinear systems over unreliable packet-based communication networks subject to random packet-dropouts. In order to mitigate the influence of the packet dropouts, the controller transmits packets containing control inputs for more than one future time instant. A suitable buffering is then applied at the plant actuator side. Since we do not assume the number of consecutive packet dropouts to be bounded, we are interested in stochastic stability of the closed-loop. For the calculation of the control inputs, we propose an unconstrained model predictive control (MPC) scheme without additional terminal weighting term. This unconstrained MPC scheme shows two significant advantages. First, we do not require the knowledge of a global control Lyapunov function, but instead only a less restrictive controllability assumption, in order to guarantee stochastic stability. Second, guaranteed performance bounds on the expected infinite horizon cost of the closed-loop can be obtained.

This work presents an unconstrained model predictive control (MPC) scheme for nonlinear time-delay systems with guaranteed closed-loop stability using neither terminal constraints nor terminal weighting terms. Therefore, we do not require the calculation of control Lyapunov-Krasovskii functionals for the nonlinear time-delay system and obtain a computationally more attractive online optimization problem. Based on similar previous results for discrete-time systems and finite-dimensional continuous-time systems, an extended asymptotic controllability assumption suitable for nonlinear time-delay systems is introduced. Since the stage cost is not positive definite in the full state, but only penalizes the instantaneous state of the system, additional arguments are required in order to guarantee closed-loop stability. It is particularly interesting to note that in contrast to essentially all other MPC schemes with guaranteed stability, the optimal cost is not used as Lyapunov function(al) of the closed-loop, and indeed the optimal cost can increase along trajectories of the closed loop due to the influence of the delayed states.

In this work we present new results on model predictive control (MPC) for nonlinear time-delay systems. In the first part we derive a novel scheme for determining a suitable terminal cost and terminal region based on the Jacobi linearization of the nonlinear system. The main advantage of the proposed scheme compared to previous results is that the terminal region is defined as a sublevel of the terminal cost functional without any restrictive requirements on the sampling time of the MPC. Based on this result, we present an MPC scheme without terminal constraint in the second part. The result extends existing results for delay-free systems and guarantees asymptotic stability of the closed-loop. The main difficulty in the derivation is to show that the integral over the stage cost has a lower bound if the state is outside of a certain region. This is directly satisfied for delay-free finite-dimensional systems, but requires additional arguments for time-delay systems.

This paper presents a continuous-time version of recent results on unconstrained nonlinear model predictive control (MPC) schemes. Based on a controllability assumption and a corresponding infinite-dimensional optimization problem, performance estimates and stability conditions are derived in terms of the prediction horizon and the sampling time of the MPC controller. Moreover, improved estimates for small sampling times are discussed and a comparison to the application of the discrete-time results in a sampled-data context is provided.

In this paper, we consider a general framework for distributed model predictive control (DMPC) of discrete-time nonlinear systems with decoupled dynamics, but subject to coupled constraints and a common, cooperative task. In contrast to most of the existing DMPC schemes in the literature, we do not necessarily consider the stabilization of an a priori known setpoint, but also other cooperative tasks like consensus and synchronization problems can be handled within the proposed framework. In order to ensure recursive feasibility and convergence to the desired cooperative goal, the systems optimize a local cost function in a sequential order, communicating their planned trajectories only to their neighbors. We exemplarily show how the proposed DMPC algorithm can be used for achieving consensus and synchronization between the systems, and we illustrate the results with a simulation example.

We consider inherent robustness properties of model predictive control (MPC) for continuous-time nonlinear systems with input constraints and terminal constraints. We show that when the linear quadratic control law is chosen as the terminal control law, and the related Lyapunov matrix is chosen as the terminal penalty matrix, MPC with nominal prediction model and bounded disturbances has some degree of inherent robustness.We emphasize that the input constraint sets can be any compact set rather than convex sets, and our results do not rely on the continuity of the optimal cost functional or control law in the interior of the feasible region.

This work presents new results on model predictive control (MPC) for nonlinear time-delay systems. In the first part, a general scheme is presented for calculating stabilizing design parameters based on the Jacobi linearization of the system. It is proven that for each system with stabilizable linearization there exist a quadratic terminal cost functional and a finite terminal region which guarantee asymptotic stability of the closed-loop. This allows the calculation of suitable design parameters for MPC based on any method available for the control of linear time-delay systems. In contrast to the delay-free case, the terminal region obtained is not characterized as sublevel set of the terminal cost functional. In the second part, a new type of terminal region is presented. Based on additional Lyapunov-Razumikhin conditions on the linear local controller it is shown that the terminal region can indeed be formulated as sublevel set of a particular terminal cost functional.

This paper proposes a novel model predictive control scheme for the stabilization of constrained linear periodically time-varying systems. The results are based on an existing Model Predictive Control scheme for uncertain linear systems using linear matrix inequalities. A pre-determined periodic feedback control law is used in combination with superimposed free control moves as additional degrees of freedom. Only the additional free control moves are calculated online taking advantage of pre-computed periodic invariant sets. Two simple algorithms are presented for calculating offline ellipsoidal or polyhedral periodic invariant sets. Since only a small number of free control moves is calculated online by solving a convex optimization problem after each time period, the computational cost can be reduced significantly compared to existing schemes.

In this work a novel procedure for the calculation of stabilizing design parameters for model predictive control of nonlinear time-delay systems is presented. In contrast to previous results, the conditions derived for the local control law and the terminal region are based only on Lyapunov Krasovskii arguments and do not require any Lyapunov Razumikhin arguments. Therefore, the conditions are less restrictive, however a more complicated terminal region is obtained. The applicability of the proposed scheme is demonstrated for the numerical model of a continuous stirred tank reactor with recycle stream.

This paper proposes a model predictive control scheme for a class of constrained nonlinear time-delay systems with guaranteed closed-loop asymptotic stability. Asymptotic stability of the closed-loop is guaranteed by utilizing an appropriate terminal cost functional and an appropriate terminal region. A novel structured procedure is derived to determine the terminal cost and the terminal region offline. For this purpose, a combination of Lyapunov-Krasovskii and Lyapunov-Razumikhin arguments is used to compute a locally stabilizing controller. The resulting conditions are formulated in terms of linear matrix inequalities.

Educational games help to increase the motivation of the students and to enhance their learning performance. For instance, educational games illustrate the link between theoretical methods presented in class and practical applications. This paper shows how an educational game based on Matlab was designed for and implemented in an advanced automatic control course at the University of Stuttgart. The different levels of the game are described that require different controller design methods. Moreover, implementational issues and didactical concepts behind this game are discussed. Finally, this game is compared to educational games developed for basic control courses.

The problem of stabilizing constrained nonlinear discrete-time periodic systems using model predictive control (MPC) is considered in this paper. The results are based on a recently developed MPC scheme for linear periodic systems which is extended to the nonlinear case by using differential inclusion. Alternatively, it can be viewed as an extension of a well-known robust MPC scheme exploiting the periodicity of the system and therefore reducing conservatism. At each time instant, a new periodic linear state feedback law is obtained based on the repeated solution of a convex optimization problem involving a set of linear matrix inequalities (LMIs). The approach can therefore take advantage of existing efficient and reliable algorithms for LMIs. A numerical example demonstrates the effectiveness of the proposed scheme.

This paper presents a new model predictive control (MPC) scheme for linear constrained discrete-time periodic systems. In each period of the system, a new periodic state feedback control law is computed via a convex optimization problem that minimizes an upper bound of an infinite horizon cost function subject to state and input constraints. The performance of the proposed model predictive controller, that stabilizes the discrete-time periodic system if it is initially feasible, is illustrated via an example.

This paper presents a new fault diagnosis scheme for parametric faults in nonlinear multivariable systems. It uses two consecutive observers, one for the state reconstruction and the second one as a reference model for the residual generation. Hence, the first one has to be robust against faults whereas the second one is sensitive to them. Faults are detected by calculating the moving norm of the difference between system output and reference model output. For fault isolation, this difference is compared to fault functions that are generated for given sets of faults. For this purpose, the moving angle serves as a measure of similarity. Moreover, small model uncertainties are considered. The theoretical results are confirmed by an simulation example.

Model predictive control (MPC) is a modern control method based on the repeated online solution of a finite horizon optimal control problem. It is particularly attractive due to its ability to take hard constraints and performance criteria directly into account. The objective of this thesis is the development of novel MPC schemes for nonlinear continuous-time systems with and without time-delays in the states which guarantee asymptotic stability of the closed-loop. The most well-studied MPC approaches with guaranteed stability use a control Lyapunov function as terminal cost. Since the actual calculation of such a function can be difficult, it is desirable to replace this assumption by a less restrictive controllability assumption. For discrete-time systems, the latter assumption has been used in the literature for the stability analysis of so-called unconstrained MPC, i.e., MPC without terminal cost and terminal constraints.

The contributions of this thesis are twofold. In the first part, we propose novel MPC schemes with guaranteed stability based on a controllability assumption, whereas we extend different MPC schemes with guaranteed stability to nonlinear time-delay systems in the second part.

In the first part of this thesis, we derive for the first time explicit stability conditions on the prediction horizon as well as performance guarantees for unconstrained MPC for continuous-time systems. Starting from this result, we propose novel alternative MPC formulations based on combinations of the controllability assumption with terminal cost and terminal constraints. Thereby, we show connections of our results to previous MPC schemes and highlight advantages. One of the main contributions is the development of a unifying MPC framework which allows to consider both MPC schemes with terminal cost and terminal constraints as well as unconstrained MPC as limit cases of our framework.

In the second part of this thesis, we show that several MPC schemes with and without terminal constraints can be extended to nonlinear time-delay systems. Due to the infinite-dimensional nature of these systems, the problem is more involved and additional assumptions are required in the controller design. For MPC schemes with terminal constraints, we prove that stability conditions similar to the delay-free case are sufficient for closed-loop stability. However, the calculation of suitable terminal cost functionals and terminal regions based on the Jacobi linearization about the origin is more difficult. We propose and investigate different procedures to overcome these difficulties. For MPC schemes without terminal constraints, we discuss MPC schemes with and without terminal cost functionals. If the terminal region is defined as a sublevel set of the terminal cost, we show that the terminal constraint can be omitted from the optimal control problem while maintaining asymptotic stability. Similar to the results in the first part of the thesis, explicit stability conditions on the prediction horizon are derived based on a modified controllability assumption suitable for time-delay systems.

Deterministic reaction models show significant shortcomings for systems with low number of particles, which are often encountered in biological processes. Their stochastic counterparts governed by the chemical master equation give a more accurate description for such systems. In most cases, the master equation is computationally intractable and Monte Carlo methods based on Gillespie's algorithms are applied instead. This thesis gives an overview of different approaches for calculating sensitivities of stochastic reaction systems with focus on sample-based methods. A new class of estimators is presented and inherent limitations for all sample-based methods are discussed.

This work presents extensions of an existing fault diagnosis algorithm to nonlinear multivariable systems with unmeasurable states. The difference of the system and a reference model is compared to the expected difference for a set of possible faults. For this purpose, the moving angle serves as a measure of similarity. The main attention was to find an algorithm that is suitable if the state is not available for measurement. Three different reference models have been investigated. Two of them apply one nonlinear observer for both state estimation and fault diagnosis whereas the third algorithm uses two consecutive observers. The theoretical results are confirmed by simulations.