In this work, two different problems are addressed. In the first part, the problem of synthesizing a set of stabilizing controllers for unknown multivariable systems using direct data is analyzed. This is a model free approach to control design and uses only the frequency domain data of the system. It is a perfect complement to modern and post modern methods that begin the control design with a system model. A three step method, involving sequential design, search for stability boundaries and stability check is proposed. It is shown through examples that a complete set of stabilizing controllers of the chosen form can be obtained for the class of linear stable multivariable systems. The complexity of the proposed method is invariant with respect to the order of the system and increases with the increase in the number of input channels of the given multivariable system. The second part of the work deals with the problem of identification of model uncertainties and the effect of unwanted exogenous inputs acting on a discrete time multivariable system using its output information. A disturbance model is introduced which accounts for the system model uncertainties and the effect of unwanted exogenous inputs acting on the system. The frequency content of the exogenous signals is assumed to be known. A linear dynamical model of the disturbance is assumed with an input that has the same frequency content as that of the exogenous input signal. The extended model of the system is then subjected to Kalman filtering and the disturbance states estimates are used to obtain a least squares estimate of the disturbance model parameters. The proposed approach is applied to a linear multivariable system perturbed by an exogenous signal of known frequency content and the results obtained depict the efficacy of the proposed approach.

Following the financial crisis of 2008, the need for more robust techniques to quantify the capital charge for risk management has become a pressing problem. Under Basel II/III, banks are allowed to calculate the capital charge using internally developed models subject to regulatory approval. An interesting problem for the regulator is to compare the resulting figures against the required capital under worst case scenarios. The existing literature on the latter problem, which is based on the marginal problem, assumes that no a-priori information is known about the dependencies of contributing risks. These problems are linear optimisation problems over a constrained set of probability measures, discretisation of which leads to large scale LPs. But this approach is very conservative and cannot be implemented robustly in practice, due to the scarcity of historical data. In our approach, we take a less conservative strategy by incorporating dependence information contained in the data in a form that still leads to LPs, an important feature of such problems due to their high dimensionality. Conceptually, our model is the discretisation of an infinite dimensional linear optimisation problem over a set of probability measures. For some specific cases we can prove strong duality, opening up the approach of discretising the dual instead of the primal. This approach is preferable, as it yields better numerical results. In this work we also apply our model to model-free path-dependent option pricing. Use of delayed column generation techniques allows us to solve problems several orders of magnitude larger than via the standard simplex algorithm. For high-dimensional LPs we also implement Nesterov's smoothing technique to solve the problems.

Conventional time series analysis depends heavily on the twin assumptions of linearity and stationarity. However; there are certain cases where sampled data tend to violate the assumptions. In this paper, we use neural networks technology to explore the situation when the assumptions of linearity and stationarity are failed. At the end of the paper, we discuss an illustrative example about the annual expenditures of government and science-education-culture of R.O.C.

Despite the vast amount of delivered theoretical results, regarding the topic of controller design, more than 90% of the controllers used in industry (petro-chemical, pulp and paper, steel, mining, etc) are of PID type (P, PI, PII, PD). This shows the importance of progressing in the elaboration of methods that consider restricted complexity controllers for practical applications, and that are computationally simple. Iterative Feedback Tuning (IFT) stands out as a new solution that takes into account both constraints. It belongs to the family of model-free controller tuning methods. It was developed at Cesame in the nineties and, since then, many real applications of IFT have been reported. This algorithm minimizes a cost function by means of a stochastic gradient descent scheme. In spite of the fact that the method has had an unexpected success in the tuning of real processes, a number of issues had not been fully covered yet. This thesis focuses on two aspects of this set of uncovered theoretical points: the convergence rate of the algorithm and a robust estimation of its gradient. Optimal prefilters, left as a degree of freedom for the user in the first formulation of IFT, are computed at each experiment. Their application allows a reduction in the covariance of the gradient estimate. Depending on what particular aspect the user is interested in improving, one optimal prefilter is selected. Monte-Carlo simulations have shown an enhancement with regards to a constant prefilter. A flexible arm set-up mounted in our robotics laboratory is used as a test bed to compare a model-based controller design algorithm with a model-free controller tuning method. The comparison is performed with some specifications defined beforehand. The same set-up plus a couple of air-jets serves as a tester for our theoretical results, when the rejection of a perturbation is the ultimate objective. Both cases have confirmed the predicted good behaviour offered by IFT.

For a long time determining the stability issue of characteristic polynomials has played avery important role in Control System Engineering. This thesis addresses the traditionalcontrol issues such as stabilizing a system with any certain controller analyzingcharacteristic polynomial, yet a new perspective to solve them. Particularly, in this thesis,Proportional-Integral-Derivative (PID) controller is considered for a fixed structuredcontroller. This research aims to attain controller gain set satisfying given performancespecifications, not from the exact mathematical model, but from the empirical data of thesystem. Therefore, instead of a characteristic polynomial equation, a speciallyformulated characteristic rational function is investigated for the stability of the systemin order to use only the frequency data of the plant. Because the performance satisfactionis highly focused on, the characteristic rational function for the investigation of thestability is mainly dealt with the complex coefficient polynomial case rather than realone through whole chapters, and the mathematical basis for the complex case is prepared.For the performance specifications, phase margin is considered first since it is avery significant factor to examine the system’s nominal stability extent (nominal performance). Second, satisfying H norm constraints is handled to make a more robustclosed loop feedback control system. Third, we assume undefined, but bounded outsidenoise, exists when estimating the system’s frequency data. While considering theseuncertainties, a robust control system which meets a given phase margin performance, isattained finally (robust performance).In this thesis, the way is explained how the entire PID controller gain setssatisfying the given performances mentioned in the above are obtained. The approachfully makes use of the calculating software e.g. MATLAB® in this research and isdeveloped in a systematically and automatically computational aspect. The result ofsynthesizing PID controller is visualized through the graphic user interface of acomputer.

For a long time determining the stability issue of characteristic polynomials has played avery important role in Control System Engineering. This thesis addresses the traditionalcontrol issues such as stabilizing a system with any certain controller analyzingcharacteristic polynomial, yet a new perspective to solve them. Particularly, in this thesis,Proportional-Integral-Derivative (PID) controller is considered for a fixed structuredcontroller. This research aims to attain controller gain set satisfying given performancespecifications, not from the exact mathematical model, but from the empirical data of thesystem. Therefore, instead of a characteristic polynomial equation, a speciallyformulated characteristic rational function is investigated for the stability of the systemin order to use only the frequency data of the plant. Because the performance satisfactionis highly focused on, the characteristic rational function for the investigation of thestability is mainly dealt with the complex coefficient polynomial case rather than realone through whole chapters, and the mathematical basis for the complex case is prepared.For the performance specifications, phase margin is considered first since it is avery significant factor to examine the system’s nominal stability extent (nominal performance). Second, satisfying H norm constraints is handled to make a more robustclosed loop feedback control system. Third, we assume undefined, but bounded outsidenoise, exists when estimating the system’s frequency data. While considering theseuncertainties, a robust control system which meets a given phase margin performance, isattained finally (robust performance).In this thesis, the way is explained how the entire PID controller gain setssatisfying the given performances mentioned in the above are obtained. The approachfully makes use of the calculating software e.g. MATLAB® in this research and isdeveloped in a systematically and automatically computational aspect. The result ofsynthesizing PID controller is visualized through the graphic user interface of acomputer.

>Magister Scientiae - MSc / This paper focuses on the newly revived interest to model free approach in finance. Instead of postulating some probability measure it emerges in a form of an outer-measure. We review the behavior of a market stock price and the stochastic assumptions imposed to the stock price when deriving the Black-Scholes formula in the classical case. Without any stochastic assumptions we derive the Black-Scholes formula using a model free approach. We do this by means of protocols that describe the market/game. We prove a statement that prices a European option in continuous time.

Control of large groups of robotic agents is driven by applications including military, aeronautics and astronautics, transportation network, and environmental monitoring. Cooperative control of networked multi-agent systems aims at driving the behavior of the group via feedback control inputs that encode the groups’ dynamics based on information sharing, with inter-agent communications that can be time varying and be spatially non-uniform. Notably, local interaction rules can induce coordinated behaviour, provided suitable network topologies. Distributed learning paradigms are often necessary for this class of systems to be able to operate autonomously and robustly, without the need of external units providing centralized information. Compared with model-based protocols that can be computationally prohibitive due to their mathematical complexity and requirements in terms of feedback information, we present an online model-free algorithm for some nonlinear tracking problems with unknown system dynamics. This method prescribes the actuation forces of agents to follow the time-varying trajectory of a moving target. The tracking problem is addressed by an online value iteration process which requires measurements collected along the trajectories. A set of simulations are conducted to illustrate that the presented algorithm is well functioning in various reference-tracking scenarios.

In recent years, the use of rotorcraft uninhabited aerial vehicles (UAVs) for cargo delivery has become of particular interest to private companies and humanitarian organizations, namely due to their reduced operational costs, ability to reach remote locations and to take off and land vertically. The slung configuration, where the cargo is suspended below the vehicle by a cable, is slowly being favoured for its ability to transport different sized loads without the need for the vehicle to land. However, such configurations require complex control systems in order to stabilize the swing of the suspended load. The goal of this research is to design a control system which will be able to bring a slung payload transported by a rotorcraft UAV back to its stable equilibrium in the event of a disturbance. A simple model of the system is first derived from first principles for the purpose of simulating a control algorithm. A controller based in model-free, policy-gradient reinforcement learning is then derived and implemented on the simulator in order to tune the learning parameters and reach a first stable solution for load stabilization in a single plane. An experimental testbed is then constructed to test the performance of the controller in a practical setting. The testbed consists of a quadcopter carrying a weight suspended on a string and of a newly designed on-board load-angle sensing device, to allow the algorithm to operate using only on-board sensing and computation. While the load-angle sensing design was found to be sensitive to the aggressive manoeuvres of the vehicle and require reworking, the proposed control algorithm was found to successfully stabilize the slung payload and adapt in real-time to the dynamics of the physical testbed, accounting for model uncertainties. The algorithm also works within the framework of the widely-used, open-source autopilot program ArduCopter, making it straightforward to implement on existing rotorcraft platforms. In the future, improvements to the load angle sensor should be made to enable the algorithm to run fully on-board and allow the vehicle to operate outdoors. Further studies should also be conducted to limit the amount of vehicle drift observed during testing of the load stabilization.

Biomass is the only renewable carbon source that can compete with fossil energy sources in terms of production of materials, chemicals and fuels. Biomass can be transformed into charcoal, liquid and gas through pyrolysis, i.e. pure thermal decomposition. By changing the pyrolysis conditions either solid, liquid or gaseous fractions can become the main product and pyrolysis is thus a very versatile process. Pyrolysis is also the first step in combustion and gasification, two important thermal processes in our society. The importance of biomass pyrolysis has led to extensive research in this area but due to the complexity of the process there is still no general understanding of how to describe biomass pyrolysis, which is essential in order to optimize thermal processes. The research presented in this thesis thus aims at finding a simple yet accurate way to model the decomposition rate of biomass during pyrolysis. Thermogravimetric analysis, a well known method that is simple to use, was chosen to collect the experimental data used for kinetic evaluation. The reaction kinetics were derived using two different model-free, isoconversional methods, i.e. the non-linear form of the Friedman method and the incremental, integral method ofVyazovkin. By using these two methods and experimental data, complete reactionrate expressions could be derived for commercial cellulose, Norway spruce and seven different samples originating from kraft cooking, the most common process to produce pulp for the paper industry. The derivation of model-free rate expressions have never been performed before for these materials and since the rate expressions are model-free, no assumptions or knowledge about the pyrolysis reactions were required. This is a great advantage compared to the commonly used model-fitting methods that rely on information about these aspects. All therate expressions were successful in predicting mass-loss rates at extrapolated pyrolysis conditions. This is a clear indication of the soundness of the methodologypresented in this thesis. / Biomassa är den enda förnybara kolkällan som kan konkurrera med fossila energikällor när det gäller produktion av material, kemikalier och bränslen. Biomassakan omvandlas till biokol, bioolja och gas med hjälp av pyrolys, dvs termisk nedbrytning. Genom att variera de processförhållanden som råder under pyrolysen kan man få antingen fast, flytande eller gasfasiga ämnen som huvudprodukt, något som gör pyrolys väldigt flexibelt. Utöver detta är pyrolys även betydelsefull vid förbränning och förgasning, två viktiga processer i dagens samhälle. Vikten av biomassapyrolys har resulterat i omfattande forskning inom området men pga biomassas komplexa natur råder det ännu ingen enighet gällande hur biomassapyrolys bör modelleras. Detta försvårar utveckling och optimering av termiska processer matade med biomassa. Forskningen som presenteras i denna avhandling fokuserar således på att finna en enkel men noggrann metod för att beskriva hastigheten med vilken biomassa bryts ned under pyrolys. Termogravimetrisk analys, en vanligt förekommande metod som är enkel att använda, valdes för att samla in experimentell data som kan användas för att undersöka hastigheten för termisk nedbrytning, dvs kinetiken. Två olika metoder som på engelska går under benämningen “model-free” och “isoconversional” har använts, nämligen den icke-linjära formen av Friedmans metod och den stegvisa, integrala metoden som utvecklats av Vyazovkin. Genom att använda dessa två metoder och experimentell data kunde kompletta reaktionshastighetsuttryck tas fram för kommersiell cellulosa, gran och sju olika material framställda genom sulfatprocessen, den idag vanligast förekommande pappersmassaprocessen. Pyrolyskinetiken för dessa material har aldrig tidigare analyserats med dessa två metoder och fördelarna med metoderna gjorde det möjligt att bestämma hastighetsuttryck utan någon kunskap om de pågående reaktionerna. Detta är en viktig fördel jämfört med andra metoder som är beroende av sådan information. Alla framtagna reaktionshatighetsuttryck kunde användas för att framgångsrikt förutsäga minskningen av massa vid extrapolerade pyrolysförhållanden. Detta är en tydlig indikation på att metoden använd i denna avhandling fungerar väl. / <p>QC 20160524</p>