In this thesis we shall investigate the numerical solutions to several important practical static and dynamic optimization problems in engineering and physics. The thesis is organized as follows.In Chapter 1 a general literature review is presented, including motivation and development of the problems, and existing results. Furthermore, some existing computational methods for optimal control problems are also discussed.In Chapter 2 the design of a semiconductor device is posed as an optimization problem: given an ideal voltage-current (V - I) characteristic, find one or more physical and geometrical parameters so that the V-I characteristic of the device matches the ideal one optimally with respect to a prescribed performance criterion. The voltage-current characteristic of a semiconductor device is governed by a set of nonlinear partial differential equations (PDE), and thus a black-box approach is taken for the numerical solution to the PDEs. Various existing numerical methods are proposed for the solution of the nonlinear optimization problem. The Jacobian of the cost function is ill-conditioned and a scaling technique is thus proposed to stabilize the resulting linear system. Numerical experiments, performed to show the usefulness of this approach, demonstrate that the approach always gives optimal or near-optimal solutions to the test problems in both two and three dimensions.In Chapter 3 we propose an efficient approach to numerical integration in one and two dimensions, where a grid set with a fixed number of vertices is to be chosen so that the error between the numerical integral and the exact integral is minimized. For one dimensional problem two schemes are developed for sufficiently smooth functions based on the mid-point rectangular quadrature rule and the trapezoidal rule respectively, and another method is also developed for integrands which are not ++ / sufficiently smooth. For two dimensional problems two schemes are first developed for sufficiently smooth functions. One is based on the barycenter rule on a rectangular partition, while the other is on a triangular partition. A scheme for insufficiently smooth functions is also developed. For illustration, several examples are solved using the proposed schemes, and the numerical results show the effectiveness of the approach.Chapter 4 deals with optimal recharge and driving plans for a battery-powered electric vehicle. A major problem facing battery-powered electric vehicles is in their batteries: weight and charge capacity. Thus a battery-powered electric vehicle only has a short driving range. To travel for a longer distance, the batteries are required to be recharged frequently. In this chapter we construct a model for a battery-powered electric vehicle, in which driving strategy is to be obtained so that the total traveling time between two locations is minimized. The problem is formulated as an unconventional optimization problem. However, by using the control parameterization enhancing transformation (CPET) (see [100]) it is shown that this unconventional optimization is equivalent to a conventional optimal parameter selection problem. Numerical examples are solved using the proposed method.In Chapter 5 we consider the numerical solution to a class of optimal control problems involving variable time points in their cost functions. The CPET is first used to convert the optimal control problem with variable time points into an equivalent optimal control problem with fixed multiple characteristic times (MCT). Using the control parameterization technique, the time horizon is partitioned into several subintervals. Let the partition points also be taken as decision variables. The control functions are approximated by piecewise constant or piecewise linear functions ++ / in accordance with these variable partition points. We thus obtain a finite dimensional optimization problem. The CPET transform is again used to convert approximate optimal control problems with variable partition points into equivalent standard optimal control problems with MCT, where the control functions are piecewise constant or piecewise linear functions with pre-fixed partition points. The transformed problems are essentially optimal parameter selection problems with MCT. The gradient formulae are obtained for the objective function as well as the constraint functions with respect to relevant decision variables. Numerical examples are solved using the proposed method.A numerical approach is proposed in Chapter 6 for constructing an approximate optimal feedback control law of a class of nonlinear optimal control problems. In this approach, the state space is partitioned into subdivisions, and the controllers are approximated by a linear combination of the 3rd order B-spline basis functions. Furthermore, the partition points are also taken as decision variables in this formulation. To show the effectiveness of the proposed approach, a two dimensional and a three dimensional examples are solved by the approach. The numerical results demonstrate that the method is superior to the existing methods with fixed partition points.

Abstract This study is based on the theory of biology and economy to establish the open access model, dynamic optimization model and static optimization of fishery mathematical models, to discuss the problem of fishery management. To be aimed at getting the equilibrium of resource stock and effort, research data are mainly analyzed by comparative statues. In so doing, the amount of grey mullet, collect and analyze the estimation of exogenous variable. Then, we can use Mathematica program to calculate the equilibrium value resource stock and the effort, and do the sensitivity analysis by standing on the change of estimation of exogenous variable. The result of analysis is as follow: These three fishery mathematical models¡¦ resource stock and effort are consistency. In another view of CPUE, it is not obvious of the economic effect of open access model. We must strengthen the management in policy of fishing for grey mullet, to let the fisherman earn the highest economic benefits. Keyword: open access model static optimization model. dynamic optimization model.

The fishery of the shrimp Acetes intermedius in the southwestern coast of Taiwan has long history , and it is the food of many species of fishes and large-scale shrimps . Shrimp Acetes has not only fallen on dead ears , but also been ignored its importantce of ecologyical status in the southwestern coast by the academia because of less harvest and output value in the past . It then comes into operation the management of catch , leading the price going up and output value increasing rapidly when the establishment of TungKang producer organization of the shrimp Acetes intrmedius in 1994 , and it also becomes the important seasonal fishery . According to as was mentioned above , the study is based on the theory of biology and economy to put out the open access model , static optimization model and dynamic optimization of fishery mathematical models , and further discuss the problem of fishery management. In connection with getting the equilibrium of resource stock and effort , research data from the substitution of real data are mainly analyzed by compareative statues on exogenous variable .By means of understanding the sensitivity of variation on endogenous variable depending on exogenous variable , we can provide the member of TungKang producer organization of the shrimp Acetes intrmedius with the control on harvest and preservation of stock . The study can get the fact that the management of TungKang producer organization of the shrimp Acetes intrmedius has the notion of sustainable administration by the deriveation of theoretical model and the simulate analysis of historyical data. I hope the management of TungKang producer organization of the shrimp Acetes intrmedius can be popularized.

The ability to stand still in one place is important in a variety of activities of daily living. For persons with motion disorders, orthopaedic treatment, which changes geometric or biomechanical properties, can improve the individual'sposture and walking ability. Decisions on such treatment require insight in how posture and walking ability are aected, however, despite expectations based on experience, it is never a-priori known how a patient will react to a treatment. As this is very challenging to observe by the naked eye, engineering tools are increasingly employed to support clinical diagnostics and treatment planning. The development of predictive simulations allows for the evaluation of the eect of changed biomechanical parameters on the human biological system behavior and could become a valuable tool in future clinical decision making. In the first paper, we evaluated the use of the Zero Moment Point as a computationally inexpensive tool to obtain the ground reaction forces (GRFs) for normal human gait. The method was applied on ten healthy subjects walking in a motion analysis laboratory and predicted GRFs are evaluated against the simultaneously measured force plate data. Apart from the antero-posterior forces, GRFs are well-predicted and errors fall within the error ranges from other published methods. The computationally inexpensive method evaluated in this study can reasonably well predict the GRFs for normal human gait without using prior knowledge of common gait kinetics. The second manuscript addresses the complications in the creation and analysis of a posture prediction framework. The fmincon optimization function in MATLAB was used in conjunction with a musculoskeletal model in OpenSim. One clear local minimum was found in the form of a symmetric standing posture but perturbation analyses revealed the presence of many other postural congurations, each representing its own unique local minimum in the feasible parameter space. For human postural stance, this can translate to there being many different ways of standing without actually noticing a difference in the efforts required for these poses. / <p>This work was financially supported by the Swedish Scientic Council(Vetenskapsrådet) grant no. 2010-9401-79187-68, the ProMobilia handicapfoundation (ref. 13093), Sunnerdahls Handicap foundation (ansökan nr 11/14),and Norrbacka-Eugenia foundation (ansökan nr 218/15).</p><p></p><p></p>

Determining tendon tension in the finger is essential to understanding forces that may be detrimental to hand function. Direct measurement is not feasible, making biomechanical modelling the best way to estimate these forces. In this study, the intrinsic muscles and extensor mechanism were added to an existing model of the index finger, and as such, it has been named the Intrinsic model. The Intrinsic model of the index finger has 4 degrees of freedom and 7 muscles (with 14 components). Muscle properties and paths for all extrinsic and intrinsic muscles were derived from the literature. Two models were evaluated, the Intrinsic model and the model it was adapted from (identified in this thesis as the Extrinsic-only model). To complement the model, multiple static optimization solution methods were also developed that allowed for EMG-constrained solutions and applied objective functions to promote co-contraction. To test the models and solution methods, 10 participants performed 9 static pressing tasks at 3 force levels, and 5 free motion dynamic tasks at 2 speeds. Kinematics, contact forces, and EMG (from the extrinsic muscles and first dorsal interosseous) were collected. For all solution methods, muscle activity predicted using the Intrinsic model was compared to activity from the model currently available through open-source software (OpenSim). Just by using the Intrinsic model, co-contraction increased by 16% during static palmar pressing tasks. The EMG-constrained solution methods gave a smaller difference between predicted and experimental activity compared to the optimization-only approach (p < 0.03). The model and solution methods developed in this thesis improve co-contraction and tendon tension estimates in the finger. As such, this work contributes to our understanding of the control of the hand and the forces that may be detrimental to hand function. / Thesis / Master of Science (MSc)

<p>At every joint there is a redundant set of muscle activated during movement or loading of the system. Optimization techniques are needed to evaluate individual forces in every muscle. The objective in this thesis was to use static optimization techniques to calculate individual muscle forces in the human extremities.</p><p>A cost function based on a performance criterion of the involved muscular forces was set to be minimized together with constraints on the muscle forces, restraining negative and excessive values. Load-sharing, load capacity and optimal forces of a system can be evaluated, based on a description of the muscle architectural properties, such as moment arm, physiological cross-sectional area, and peak isometric force.</p><p>The upper and lower extremities were modelled in two separate studies. The upper extremity was modelled as a two link-segment with fixed configurations. Load-sharing properties in a simplified model were analyzed. In a more complex model of the elbow and shoulder joint system of muscular forces, the overall total loading capacity was evaluated.</p><p>A lower limb model was then used and optimal forces during gait were evaluated. Gait analysis was performed with simultaneous electromyography (EMG). Gait kinematics and kinetics were used in the static optimization to evaluate of optimal individual muscle forces. EMG recordings measure muscle activation. The raw EMG data was processed and a linear envelope of the signal was used to view the activation profile. A method described as the EMG-to-force method which scales and transforms subject specific EMG data is used to compare the evaluated optimal forces.</p><p>Reasonably good correlation between calculated muscle forces from static optimization and EMG profiles was shown. Also, the possibility to view load-sharing properties of a musculoskeletal system demonstrate a promising complement to traditional motion analysis techniques. However, validation of the accurate muscular forces are needed but not possible.</p><p>Future work is focused on adding more accurate settings in the muscle architectural properties such as moment arms and physiological cross-sectional areas. Further perspectives with this mathematic modelling technique include analyzing pathological movement, such as cerebral palsy and rheumatoid arthritis where muscular weakness, pain and joint deformities are common. In these, better understanding of muscular action and function are needed for better treatment.</p>

At every joint there is a redundant set of muscle activated during movement or loading of the system. Optimization techniques are needed to evaluate individual forces in every muscle. The objective in this thesis was to use static optimization techniques to calculate individual muscle forces in the human extremities. A cost function based on a performance criterion of the involved muscular forces was set to be minimized together with constraints on the muscle forces, restraining negative and excessive values. Load-sharing, load capacity and optimal forces of a system can be evaluated, based on a description of the muscle architectural properties, such as moment arm, physiological cross-sectional area, and peak isometric force. The upper and lower extremities were modelled in two separate studies. The upper extremity was modelled as a two link-segment with fixed configurations. Load-sharing properties in a simplified model were analyzed. In a more complex model of the elbow and shoulder joint system of muscular forces, the overall total loading capacity was evaluated. A lower limb model was then used and optimal forces during gait were evaluated. Gait analysis was performed with simultaneous electromyography (EMG). Gait kinematics and kinetics were used in the static optimization to evaluate of optimal individual muscle forces. EMG recordings measure muscle activation. The raw EMG data was processed and a linear envelope of the signal was used to view the activation profile. A method described as the EMG-to-force method which scales and transforms subject specific EMG data is used to compare the evaluated optimal forces. Reasonably good correlation between calculated muscle forces from static optimization and EMG profiles was shown. Also, the possibility to view load-sharing properties of a musculoskeletal system demonstrate a promising complement to traditional motion analysis techniques. However, validation of the accurate muscular forces are needed but not possible. Future work is focused on adding more accurate settings in the muscle architectural properties such as moment arms and physiological cross-sectional areas. Further perspectives with this mathematic modelling technique include analyzing pathological movement, such as cerebral palsy and rheumatoid arthritis where muscular weakness, pain and joint deformities are common. In these, better understanding of muscular action and function are needed for better treatment. / QC 20101116

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Cílem práce byl návrh a implementace řídicích algoritmů pro optimalizaci spotřeby energie elektrického vozidla. Hlavním úkolem byla optimalizace rozložení energie mezi hlavním zdrojem energie (bateriemi) a super-kapacitory v průběhu jízdního cyklu. Jízdní výkonový profil je odhadován a předpovězen na základě 3D geografických souřadnic a matematického modelu vozidla. V první části jsou uvedeny komponenty vozidla a jejich modely. Poté jsou představeny algoritmy na základě klouzavého průměru a dynamického programování. Byly provedeny simulace a analýzy pro demostraci přínosů algoritmů. V poslední části je popsána Java implementace algoritmů a také aplikace pro operační systém Android.

Cílem práce byl návrh a implementace řídicích algoritmů pro optimalizaci spotřeby energie elektrického vozidla. Hlavním úkolem byla optimalizace rozložení energie mezi hlavním zdrojem energie (bateriemi) a super-kapacitory v průběhu jízdního cyklu. Jízdní výkonový profil je odhadován a předpovězen na základě 3D geografických souřadnic a matematického modelu vozidla. V první části jsou uvedeny komponenty vozidla a jejich modely. Poté jsou představeny algoritmy na základě klouzavého průměru a dynamického programování. Byly provedeny simulace a analýzy pro demostraci přínosů algoritmů. V poslední části je popsána Java implementace algoritmů a také aplikace pro operační systém Android.