<p>This thesis concerns modeling and control of bilinear systems (BLS). BLS are linear but not jointly linear in state and control. In the first part of the thesis, a background to BLS and their applications to modeling and control is given. The second part, and likewise the principal theme of this thesis, is dedicated to theoretical aspects of identification, modeling and control of mainly BLS, but also linear systems. In the last part of the thesis, applications of bilinear and linear modeling and control to the activated sludge process (ASP) are given.</p>

Integrodifference equations are discrete in time and continuous in space, and are used to model the spread of populations that are growing in discrete generations, or at discrete times, and dispersing spatially. We investigate optimal harvesting strategies, in order to maximize the profit and minimize the cost of harvesting. Theoretical results on the existence, uniqueness and characterization, as well as numerical results of optimized harvesting rates are obtained. The order of how the three events, growth, dispersal and harvesting, are arranged also affects the harvesting behavior. Cholera remains a public health threat in many parts of the world and improved intervention strategies are needed. We investigate a key intervention strategy, vaccination, with optimal control applied to a cholera model. This system of differential equations has human compartments with susceptibles with different levels of immunity, symptomatic and asymptomatic infecteds, and two cholera vibrio compartments, hyperinfectious and non-hyperinfectious. The spread of the infection in the model is shown to be most sensitive to certain parameters, and the effect of varying these parameters on the optimal vaccination strategy is shown in numerical simulations. Our simulations also show the importance of the infection rate under various parameter cases.

This dissertation presents various research contributions published during these four years of PhD in the field of batch mode reinforcement learning, which studies optimal control problems for which the only information available on the system dynamics and the reward function is gathered in a set of trajectories. We first focus on deterministic problems in continuous spaces. In such a context, and under some assumptions related to the smoothness of the environment, we propose a new approach for inferring bounds on the performance of control policies. We also derive from these bounds a new inference algorithm for generalizing the information contained in the batch collection of trajectories in a cautious manner. This inference algorithm as itself lead us to propose a min max generalization framework. When working on batch mode reinforcement learning problems, one has also often to consider the problem of generating informative trajectories. This dissertation proposes two different approaches for addressing this problem. The first approach uses the bounds mentioned above to generate data tightening these bounds. The second approach proposes to generate data that are predicted to generate a change in the inferred optimal control policy. While the above mentioned contributions consider a deterministic framework, we also report on two research contributions which consider a stochastic setting. The first one addresses the problem of evaluating the expected return of control policies in the presence of disturbances. The second one proposes a technique for selecting relevant variables in a batch mode reinforcement learning context, in order to compute simplified control policies that are based on smaller sets of state variables.

Trucks are responsible for the major part of inland freight and so, they are a backbone of the modern economy but they are also a large consumer of energy. In this context, a dominating vehicle is a truck with heavy load on a long trip. The aim with look-ahead control is to reduce the energy consumption of heavy vehicles by utilizing information about future conditions focusing on the road topography ahead of the vehicle. The possible gains with look-ahead control are evaluated by performing experiments with a truck on highway. A real-time control system based on receding horizon control (RHC) is set up where the optimization problem is solved repeatedly on-line for a certain horizon ahead of the vehicle. The experimental results show that significant reductions of the fuel consumption are achieved, and that the controller structure, where the algorithm calculates set points fed to lower level controllers, has satisfactory robustness to perform well on-board in a real environment. Moreover, the controller behavior has the preferred property of being intuitive, and the behavior is perceived as comfortable and natural by participating drivers and passengers. A well-behaved and efficient algorithm is developed, based on dynamic programing, for the mixed-integer nonlinear minimum-fuel problem. A modeling framework is formulated where special attention is given to properly include gear shifting with physical models. Fuel equivalents are used to reformulate the problem into a tractable form and to construct a residual cost enabling the use of a shorter horizon ahead of the vehicle. Analysis of errors due to discretization of the continuous dynamics and due to interpolation shows that an energy formulation is beneficial for reducing both error sources. The result is an algorithm giving accurate solutions with low computational effort for use in an on-board controller for a fuel-optimal velocity profile and gear selection. The prevailing approach for the look-ahead problem is RHC where main topics are the approximation of the residual cost and the choice of the horizon length. These two topics are given a thorough investigation independent of the method of solving the optimal control problem in each time step. The basis for the fuel equivalents and the residual cost is formed from physical intuition as well as mathematical interpretations in terms of the Lagrange multipliers used in optimization theory. Measures for suboptimality are introduced that enables choosing horizon length with the appropriate compromise between fuel consumption and trip time. Control of a hybrid electric powertrain is put in the framework together with control of velocity and gear. For an efficient solution of the minimum-fuel problem in this case, more fuel equivalence factors and an energy formulation are employed. An application is demonstrated in a design study where it is shown how the optimal trade-off between size and capacity of the electrical system depends on road characteristics, and also that a modestly sized electrical system achieves most of the gain. The contributions develop algorithms, create associated design tools, and carry out experiments. Altogether, a feasible framework is achieved that pave the way for on-board fuel-optimal look-ahead control.

Novel event-triggered sensing and actuation strategies are presented for networked control systems with limited communication resources. Two architectures are considered: one with the controller co-located with the sensor and one with the control co-located with the actuator. A stochastic control problem with an optimal stopping rule is shown to capture two interesting instances of these architectures. The solution of the problem leads to a parametrization of the control alphabet as piecewise constant commands. The execution of the control commands is triggered by stopping rules for the sensor. In simple situations, it is possible to analytically derive the optimal controller. Examples illustrate how the new event-based control and sensing strategies outperform conventional time-triggered schemes. / <p>© 2008 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. Qc 20120220</p>

Positive systems, which carry the well known property of confining the state, output, and/or input variables to the nonnegative orphant, are of great practical importance, as the nonnegative property occurs quite frequently in numerous applications and in nature. These type of systems frequently occur in hydrology where they are used to model natural and artificial networks of reservoirs; in biology where they are used to describe the transportation, accumulation, and drainage processes of elements and compounds like hormones, glucose, insulin, and metals; and in stocking, industrial, and engineering systems where chemical reactions, heat exchanges, and distillation processes take place. The interest of this dissertation is in two key problems: positive stabilization and the positive servomechanism problem. In particular, this thesis outlines the necessary and sufficient conditions for the stabilization of positive linear time-invariant (LTI) systems using state feedback control, along with providing an algorithm for constructing such a stabilizing regulator. Moreover, the results on stabilization also encompass the two problems of the positive separation principle and stabilization via observer design. The second, and most emphasized, problem of this dissertation considers the positive servomechanism problem for both single-input single-output (SISO) and multi-input multi-output (MIMO) stable positive LTI systems. The study of the positive servomechanism problem focuses on the tracking problem of nonnegative constant reference signals for unknown/known stable SISO/MIMO positive LTI systems with nonnegative unmeasurable/measurable constant disturbances via switching tuning clamping regulators (TcR), linear quadratic clamping regulators (LTQcR), and ending with MPC control. Finally, all theoretical results on the positive servomechanism problem are justified via numerous experimental results on a waterworks system.

This thesis deals with the design of multivariable controllers for stable linear time-invariant multi-input multi-output systems, with an unknown mathematical model, subject to constant reference/disturbance signals and actuator saturation constraints. A new controller parameter optimization approach, which can be carried out experimentally with no knowledge of the plant model nor of the order of the system, is proposed. The approach has the advantage that controllers can be optimized by perturbing only the initial conditions of the servocompensator, and that the order of the resulting controller obtained can be specified by the designer. Implementation of the proposed controller design approach is described, and an experimental application study of the proposed method applied to a multivariable system with industrial sensor/actuator components is presented to illustrate the feasibility of the design method in an industrial environment.

This thesis deals with the design of multivariable controllers for stable linear time-invariant multi-input multi-output systems, with an unknown mathematical model, subject to constant reference/disturbance signals and actuator saturation constraints. A new controller parameter optimization approach, which can be carried out experimentally with no knowledge of the plant model nor of the order of the system, is proposed. The approach has the advantage that controllers can be optimized by perturbing only the initial conditions of the servocompensator, and that the order of the resulting controller obtained can be specified by the designer. Implementation of the proposed controller design approach is described, and an experimental application study of the proposed method applied to a multivariable system with industrial sensor/actuator components is presented to illustrate the feasibility of the design method in an industrial environment.

In this thesis, energy optimal route of an unmanned solar powered air vehicle is obtained for the given mission constraints in order to sustain the maximum energy balance. The mission scenario and the constraints of the solar powered UAV are defined. Equations of motion are obtained for the UAV with respect to the chosen structural properties and aerodynamic parameters to achieve the given mission. Energy income and loss equations that state the energy balance, up to the position of the UAV inside the atmosphere are defined. The mathematical model and the cost function are defined according to the mission constraints, flight mechanics and energy balance equations to obtain the energy optimal path of the UAV. An available optimal control technique is chosen up to the mathematical model and the cost function in order to make the optimization. Energy optimal path of the UAV is presented with the other useful results. Optimal route and the other results are criticized by checking them with the critical positions of the sun rays.

Control of the transition of laminar flow to turbulence would result in lower drag and reduced energy consumption in many engineering applications. A spectral state-space model of linearised plane Poiseuille flow with wall transpiration ac¬tuation and wall shear measurements is developed from the Navier-Stokes and continuity equations, and optimal controllers are synthesized and assessed in sim¬ulations of the flow. The polynomial-form collocation model with control by rate of change of wall-normal velocity is shown to be consistent with previous interpo¬lating models with control by wall-normal velocity. Previous methods of applying the Dirichlet and Neumann boundary conditions to Chebyshev series are shown to be not strictly valid. A partly novel method provides the best numerical behaviour after preconditioning. Two test cases representing the earliest stages of the transition are consid¬ered, and linear quadratic regulators (LQR) and estimators (LQE) are synthesized. Finer discretisation is required for convergence of estimators. A novel estimator covariance weighting improves estimator transient convergence. Initial conditions which generate the highest subsequent transient energy are calculated. Non-linear open- and closed-loop simulations, using an independently derived finite-volume Navier-Stokes solver modified to work in terms of perturbations, agree with linear simulations for small perturbations. Although the transpiration considered is zero net mass flow, large amounts of fluid are required locally. At larger perturbations the flow saturates. State feedback controllers continue to stabilise the flow, but estimators may overshoot and occasionally output feedback destabilises the flow. Actuation by simultaneous wall-normal and tangential transpiration is derived. There are indications that control via tangential actuation produces lower highest transient energy, although requiring larger control effort. State feedback controllers are also synthesized which minimise upper bounds on the highest transient energy and control effort. The performance of these controllers is similar to that of the optimal controllers.