# Usage This page summarizes the usage of {{osyn}}. Further detail on the {{osyn}} workflow is available in subsequent pages: ```{toctree} :maxdepth: 1 Build the System Simulate Problem Setup Solve and Validate ``` All code is written in object-oriented MATLAB. The {doc}`Documentation <../documentation/index_documentation>` page contains details about each object and function. ## Tasks The three main tasks of {{osyn}} are Simulation, Analysis, and Synthesis. Simulation solves an inclusion algorithm $0 \in \sum_{i=1}^{s} F_i(\beta^*)$ by iteratively executing an algorithm. Analysis certifies worst-case performance specifications of the algorithm for any $F_i$ in given classes of operators. Synthesis creates a controller such that the overall algorithm obeys the desired performance specifications. All three tasks model the algorithm as a System ({class}`opt_system`). The System has three main parts: the operators, the network, and the controller. ```matlab sys = opt_system(Operators, Network, Controller); ``` The operators are specified as an $s$-length cell array. These are specific operators $F_i$ in Simulation ({class}`op_sim`), or are operator classes in Analysis/Synthesis (e.g. {class}`op_gen` for set-valued maps, {class}`op_quad` for quadratics). The network and controller are both state-space dynamical systems. These are represented through a Generalized Plant construction as {class}`genplant` objects. ## Simulation Simulation is conducted by the {class}`alg_sim` object. The first $T$ time steps of executing a $d$-dimensional inclusion algorithm is accomplished by ```matlab simulator = alg_sim(sys, d); sim_result = simulator.sim(T); ``` The output of simulation can then be plotted by {class}`alg_plotter` ```matlab plt = alg_plotter(sim_result); fig1 = plt.plot({'w', 'z'}); %or other desired signals. ``` ## Analysis and Synthesis Analysis and Synthesis programs are declared by manager objects ```matlab man_ana = opt_analysis(sys); man_syn = opt_synthesis(sys); ``` The Analysis and Synthesis problems are specified by the configuration options ({class}`opt_config`), and performance specifications. They are solved by using the {meth}`solve_single`, {meth}`bisect`, or {meth}`alternate` commands. Increasing the `order` yields tighter bounds, at the cost of more computationally intensive programs. ```matlab sol = man_ana.bisect(order, specs); %specs: cell array of specifications sol = man_syn.bisect(); %empty: default to linear convergence with rate 1 sol = man_syn.bisect(iqc, specs); %warm-start with previous Analysis solution (iqc) sol = man_syn.alternate(Niteration, order); %alternate between Synthesis and Analysis ``` The output is stored in the solution object `sol`. Fields of `sol` include `sol.rho` (convergence rate), `sol.sys` (overall system), and `sol.objective` (optimization target).