## Practical output regulation

Practical output regulation is defined to overcome the main difficulties in the nonlinear output regulation problem that is, finding the solution of the regulator equations (and suitable immersed map in output feedback case). The main goal is finding a method to approximate solution to these partial differential equation for general finite dimensional nonlinear systems, excited by a class of exogenous systems. Possibly relation between approximation specification and closed-loop specifications, should be revealed then to achieve a systematic approach for the purpose of finding practical nonlinear output regulators.

## Controller Design for Monotone Systems

Monotone dynamical systems constitute one of the most important classes in the ground of biological modeling and analysis. To date, monotone systems have been studied from the analysis viewpoint, whereas control design for such dynamical systems has not been considerably remarked. Control design may be so valuable in practice for nonlinear monotone systems with a little known dynamic information. The thesis tries to set up a control design framework to capture closed loop systems with desired dynamical characteristics. The theorems at hand for analyzing monotone autonomous systems may help in this regard. To evaluate the resulting framework, a nonlinear model of cancer cells growth (which is a monotone I/O system) from literature is employed. The goal is to navigate the system from every initial point in the state space into the region of attraction of healthy equilibrium point.

Boundedness of the solutions while keeping the system away from (biologically) dead null space of the system is needed. The input, here, can be the doze of injecting drug, while the output is population of tumor cells in a tissue under experiment.

## Switching between active & passive mechanisms in mobile robots

Working on bipedal robot walking is the subject of researches in many high quality robotic institutes. The variety of methods applied to generate desirable walking is noteworthy. In spite of existence of so many attitudes in this field, stability analysis of such a complex dynamic system is rarely attracted the attention of researchers. In order to guarantee the control performance and expanding concepts like optimality or robustness, stability proofs are inevitable. Between some stability analysis mechanisms which are in the literature, HZD (Hybrid Zero Dynamics) was selected to design and investigate the controller for bipedal walker robots in this thesis. Our approach to control the bipedal walking robot is shaping its dynamics via insertion of some semi-passive physical elements like springs or dampers to generate a stable locomotion. In other words, when the zero dynamics of the controlled robot is unstable, then the possible solutions to stabilize them are output redefinition and/or restructuring the robot body like insertion of some compliant mechanisms.

## Stability Analysis and Control of Nonlinear Hybrid Systems

Hybrid systems are complex systems which combine both continuous-time dynamic and discrete-time dynamic (modes). Also, many natural and artificial systems and processes have several modes of operation with a different dynamical behavior in each mode, so these systems and processes can be modeled mathematically as hybrid systems or switched systems. Therefore stability analysis and control of the systems is important for both theoretical and practical reasons. Although we study stability analysis and control of nonlinear hybrid systems, we study many problems that can be modeled by hybrid systems, as networked control systems (NCS).

## Desynchronization of coupled oscillators

Synchronization is one of the most interesting patterns in systems composed of many dynamical components such as neuronal populations. Although, synchronization of different neurons plays an important role in biological information processing and rhythmical activity, several neurological diseases (e.g., essential tremor and Parkinson's disease) are related to pathologically enhanced synchronization of bursting neurons. So, designing a demand controller to suppress the collective synchrony seems crucial.

## Control of Time Delay Systems

Delays are among the most common dynamic phenomena arising in control engineering practice. Interest in delay systems is driven by applications such as chemical process control, machining, combustion systems, teleoperation, and networked systems. Delay systems belong to the class of distributed para meter systems but have a special structure, not possessed by partial differential equations, that can be exploited in analysis and design to arrive at compact or even explicit solutions. An enormous wealth of results exists for controlling systems with state, input, and output delays. Control problems with input delays are among the earliest challenges to be tackled.

## Enlarging domain of attraction in nonlinear control systems

For a controlled system, it's not enough to be locally asymptotically stable at equilibrium point. In addition initial states of system result in equilibrium points are also significant and entitle as "domain of attraction" of a dynamic system. In spite of long history of research on this topic, until now there's no general analytic method for determination of domain of attraction. Approximate methods have own restrictions and albeit have own advantageous. Improvement in analytic or approximate methods is beneficial and we try to.

## Modeling and control of nonholonomic mechanical systems

In robotics, especially in mobile robots, nonholonomic constraints appear in dynamical equations of motion. In routine methods of modeling, these constraints increase the number of equations that describe the motion of a nonholonomic system. Notably in complex multi-body robots, it causes considerable effects on processing time and control. Using some advanced methods, such as Gibbs-Appell and Kane, we are able to reduce the required number of differential equations. In these methods, suitable selection of dynamical variables is important. We study the relation between the selection of dynamical variables and the simplification of optimal control problem for nonholonomic mechanical systems.

## Feet role in bipedal robot locomotion

The main motivation of working on bipedal robots is substituting them with human in hazardous situations. More similarity of human with robot results in more possibility of the mentioned substitution. The problem of having a stable motion is the main challenge of controlling a legged robot. Among several control methods of bipedal robot, Hybrid Zero Dynamics (HZD) is selected in this thesis for its profound background in the literature. In this method, the notion of walking is defined as the stability of dynamic model of the robot equilibrium by some algebraic equations. By transforming of the walking problem in a control problem structure, it is provided to consider robustness, optimality, etc. In this thesis, it is tried to benefit nonlinear methods in analysis of the designed controller. So, zero dynamics analysis, Poincare map, hybrid system analysis, optimization on path planning and output regulation are considered. Also, the Jacobian of Poincare map provides criteria for robustness. Besides derivation of the dynamic equation of a bipedal robot with leg compliant and curvy feet, the main contribution of the thesis is the type of our attitude to existence of the curve feet. This feature not only makes the robot more similar with human, but also, it resembles prosthetic feet and the results of these analysis are useful in constructing prosthesis. Consideration of the curve feet existence on stability, robot velocity, energy consumption and robustness against parametric uncertainty and external disturbances are the main achievements of the thesis.

## Power Systems Transient Stability Domain Analysis

Traditional analysis and control techniques for power systems are undergoing a major reassessment in recent years. This worldwide trend is driven by multiple factors including the adoption of new technologies, which offer improvements in power angle and voltage stability but give rise to many modeling and control issues that remain to be resolved. With increased pressure to maximize power transfers, electric utilities are being pushed to operate their systems much closer to their stability limits. Thus, fast transient stability analysis plays an important role in power system planning. Analysis of the stability of power systems following a transient disturbance involves the study of a large set of nonlinear differential equations. Transient stabilization has been traditionally formulated in terms of enlarging the domain of attraction of an operating equilibrium point, approach that has been widely adopted by the control community.

## Nonlinear Model Reduction

Model order reduction (MOR) is a very powerful technique that is used to deal with the increasing complexity of dynamic systems and aim at approximating a complex system by a simpler system, while preserving, as much as possible, input-output properties of this system. It is a mature and well understood field of study that has been applied to large linear dynamic systems with great success. However, high fidelity modeling of complex physical phenomena that results in nonlinear dynamical systems with very large complexity, has forced designers to consider nonlinear effects for more accurate model representations. This has created the need for a methodology to generate compact models from nonlinear systems of high dimensionality, since only such a solution will give an accurate description for current and future complex systems.