An iterative learning algorithm is presented for continuous-time linear–quadratic optimal control problems where the system is externally symmetric with unknown dynamics. Both finite-horizon and infinite-horizon problems are considered. It is shown that the proposed algorithm is globally convergent to the optimal solution and has some advantages over adaptive dynamic programming, including unbiased performance under noisy measurements, relatively low computational burden, and no requirement for exploration noise. Numerical experiments show the effectiveness of the results.

We study how neural networks can perform the task of elevator dispatching of commuters from their origins to their destinations. Instead of applying a neural network in the conventional way, we construct a specific neural network architecture that optimizes the commuters’ traveling time after taking into account the domain knowledge and the efficacy of potential future actions. The constructed architecture is modular with building blocks of neuronal structure that serve specified functional roles. By relaxing the weights and then training this network via reinforcement learning, we show that it outperforms an agent that implements the standard elevator algorithm. More remarkably, we observe the spontaneous emergence of functional modules within the structure of the network in consequence of the action sequences experienced during training. This behavioral feature of the neural network makes it less of a black box, with specific aspects of its functions being explicitly discernible from its network connections.

Monotonic tracking is required in many control systems, including those that cannot tolerate any overshoots and undershoots in their closed-loop responses. Classical examples are found in vehicle cruise control and liquid tank level control. In the former, an overshoot happens when the speed of the vehicle goes beyond the set value violating the safety measures, and in the latter an overshoot is considered as filling up the tank with an excessive amount of liquid which leads to a waste of resources. Controllers that eliminate overshoots are undeniably more desirable in these examples. In fact, the same requirement is in place for many more engineering applications, including biological systems, robotics and process control, indicating widespread benefits of controllers which can guarantee monotonicity in the system response. Formally, linear systems that exhibit monotonically increasing step responses are called externally positive. Designing controllers that render the closed-loop system externally positive requires a thorough understanding of this property in linear systems. In this thesis, we leverage combinatorial polynomials and their properties to study external positivity in both discrete-time and continuous-time linear systems modelled by transfer functions or impulse responses. Several conditions are provided that are either necessary, sucientor both necessary and sufficient for a linear system to be externally positive. These conditions are then used to synthesize controllers that ensure external positivity in closed-loop systems and hence, eliminate both overshoots and undershoots in the system response. In particular, we provide synthesis techniques based on convex optimization that ensure stability, robustness and offset-free monotonic tracking in the closed-loop system and improve its decay rate and sensitivity. We compare the results with the state-of-the-art in the literature and demonstrate the efficacy of the proposed controller synthesis methods through several numerical examples.

Monoton styrning krävs i många reglersystem, däribland de som inte kan hantera över- eller underskjutningar i sina slutna systemsvar. Typexempel återfinns inom fartreglering av fordon och nivåreglering av vätsketankar. I det förstnämnda exemplet inträffar en överstyrning när fordonets hastighet överskrider det inställda värdet, och bryter mot säkerhetskrav, och i det senare betraktas en överstyrning som att fylla tanken med för mycket vätska vilket resulterar i resursslöseri. Regulatorer som eliminerar över- och underskjutningar är otvivelaktigt mer önskvärda i dessa exempel. Detta gäller även för flera andra tekniska tillämpningar, inklusive biologiska system, robotik och processkontroll, vilket indikerar stora fördelar med regulatorer som kan garantera monotonicitet i systemsvaret inom många domäner.

Formellt kallas linjära system som uppvisar monotont ökande stegsvar \emph{externally positive}. För att utforma regulatorer som garanterar att det åter-koppladde systemet är externt positivt krävs en bättre förståelse av hur denna egenskap karaktäriseras för linjära system. Därför använder vi i denna avhandling kombinatoriska polynom och deras egenskaper för att studera extern positivitet både för diskreta och kontinuerliga linjära system modellerade av överföringsfunktioner eller impulssvar. Med hjälp av dessa polynom härleds flera villkor som antingen är nödvändiga, tillräckliga eller både nödvändiga och tillräckliga för att ett linjärt system ska vara externt positivt. Dessa villkor inkorporeras sedan för att syntetisera reglersystem som säkerställer extern positivitet i återkopplade system och därmed eliminera både över- och underskjutningar i systemsvaret. Särskilt tillhandahåller vi syntesmetoder baserade på konvex optimering som säkerställer stabilitet, robusthet och offset-fri monoton styrning för slutna systemet och förbättrar dess avklingningshastighet och känslighet. Vi jämför resultaten med det bästa tillgängliga i litteraturen och visar effektiviteten hos de föreslagna syntesmetoderna genom flera numeriska exempel.

The problem of learning-to-control relaxation systems from data is considered. It is shown that the equi-librium of the relaxation system's step response defines the solution of a class of robust control problems and provides a good suboptimal solution to a class of linear quadratic regulator problems. These results demonstrate the potential to efficiently learn policies for these control problems from a single, easy-to-implement trajectory data point, being the step response. More broadly, these results highlight how the system structure and problem definition of the control problem can be exploited to generate data efficient learning- to-control methods.

This article develops an optimization-based synthesis procedure for fixed-order output-feedback controllers, ensuring a stable closed-loop system with a monotonic step response and rejection of persistent disturbances. This result is based on a unified set of external positivity conditions for discrete-time linear systems. The conditions are derived using an alternative technique for the inverse Z-transform of rational transfer functions based on Bell polynomials and a convenient recurrence relation for the impulse response. Our approach yields a necessary and sufficient condition expressed as polynomial inequalities in the transfer function coefficients. Under additional assumptions, we derive a sequence of weaker but numerically more tractable conditions, leading to an efficient controller synthesis procedure.

This paper presents informative battery charging, a novel approach for battery model parameter estimation during fast charge. Our solution comprises three distinct contributions: first, we develop a semi-explicit solution to an optimal fast charging problem for equivalent circuit models with health-conscious voltage constraints; second, we design optimal experiments for battery model parameter estimation; and third, we suggest a strategy for how the fast charging and experimentation currents can be combined while still satisfying constraints and maintaining acceptable charging times. Numerical results show that model parameters can be identified with lower variance if an optimal experiment is added to the charging procedure.

This paper studies the class of logarithmically completely monotonic (LCM) functions. These functions play an important role in characterizing externally positive linear systems which find applications in important control problems such as non-overshooting reference tracking. Conditions are proposed to ensure a rational function is LCM, a result that enables the known space of linear continuous-time externally positive systems to be enlarged and an efficient and optimal pole-placement procedure for the monotonic tracking controller synthesis problem to be developed. The presented conditions are shown to be less conservative than existing approaches whilst being computationally tractable.

This paper presents a technique for designing twoparameter compensators that stabilize a plant and provide offset-free tracking of set-points without overshooting or undershooting. We first represent the impulse response of linear systems using combinatorial polynomials, based on which a new set of conditions is derived for the system to be externally positive. This result is then used in control synthesis to achieve monotonic tracking. In contrast to the methods available in the literature, the proposed technique always gives a solution whenever the problem is feasible, can yield as small a settling time as desired, and provides the freedom to choose the closedloop poles arbitrarily inside the unit circle, all obtained by low-degree controllers.

Several time-domain constraints for linear systems are characterized using a new representation of the impulse response based on symmetric polynomials. This includes the induced infinity-norm, the peak response and external positivity - performance indices that are complicated to impose in existing LMI frameworks. Each index is described by a convex constraint, explicit in terms of the system poles. Despite their simplicity, numerical examples suggest that these constraints can provide relatively tight performance bounds.

Robust stability problem of integral delay systems with uncertain kernel matrix functions is addressed in this paper. On the basis of the characteristic equation and the argument principle, an algorithm is generated, which is shown to outperform the Lyapunov-Krasovskii (LK) approaches with respect to conservatism in the presented examples. Despite the conventional manual use of the Nyquist criterion, the proposed algorithm is fully algebraic, cheaper and easily implemented in computer programs. The kernel matrix function in this method is not limited to the exponential type and can include any bounded real function as its elements.